Andrzej Pelczar



(100th anniversary of taking up a chair at the Jagiellonian University)


    1. Some remarks on the historical background; Kraków scientific centre.

    Since the XVIII-th century, owing to the significant activity of Jan Śniadecki  (1756-1830) and reforms made by him, there were two chairs of mathematics at the Jagiellonian University in Kraków. Various people, representing various level of knowledge and competence had chaired them during almost one hundred years, till the end of the XIX-th century, when two outstanding mathematicians, Kazimierz Żorawski in 1895 and Stanisław Zaremba in 1900, came to Kraków and begun a new period of  the research and teaching in mathematics, not only at the oldest Polish University but also in the whole country. Let us recall that it was a difficult time in Polish history. Poland had been partitioned in 1772; three empires : Russia, Austria and Prussia controlled three parts of the country. Situation in the Austrian part was relatively less bad than in the two other parts; in particular, in the last quarter of the nineteenth century Kraków was a real centre of the Polish culture and the Jagiellonian University was really a Polish University. These circumstances made in practice Żorawski and Zaremba almost the only representatives of  Polish mathematics on international arena for more than one and half decade..

     Before talking in detail on the activity of the hero of this presentation, Stanisław Zaremba, we will give some general information on the scientific centre built up by these two professors.

     Kazimierz Paulin Żorawski (1866-1953) was a student of Sophus Lie and brought  fundamental ideas of his master, of course first of all those related to theory of continuous groups (called now Lie groups), implementing them creatively in Kraków. He developed also several areas close to the theory of Lie groups and based on it, in particular certain parts of the theory of differential equations and differential geometry, as well as some topics from the theory of integral invariants (new at that time), selected problems from kinematics and some other fields (compare for instance [17]).

     Stanisław Zaremba (1863-1942) graduated firstly as an engineer in St. Petersburg studied later on mathematics in Paris, getting there his Ph.D. In the Ph.D. thesis “Sur un problème concernant l’état calorifique d’un corps homogène indefini” he presented a solution to a problem posed by the Paris Academy of Sciences. He improved essentially some non-complete results concerning that problem announced earlier by Riemann. This thesis determined in a sense his future scientific career and described the field of interest.

     None of the two outstanding scientists created a classical “scientific school” in a narrow meaning of this name, but they had built up a true scientific centre being a real basis for future scientific schools of their pupils. Kazimierz Żorawski was the supervisor of the Ph.D. thesis of Franciszek Leja (1885-1979); among his pupils there were Władysław Ślebodziński (1884-1972) and Antoni Hoborski (1879-1940) who was simultaneously scientifically close to Zaremba, obtaining Ph.D. and habilitation under Zaremba’s supervision, and then turning to differential geometry, the field from Żorawski’s general area of interest. Thus Hoborski should be counted as a pupil of both professors, or rather as a student who was a member of a scientific centre being created at that time by them (Hoborski was later on the first rector of the Academy of Mining erected in 1919; he died in the concentration camp Sachsenhausen in February 1940 being arrested by nazi occupants together with the majority of professors of the Jagiellonian University and Academy of Mining on November 6, 1939). Zaremba was also the supervisor of Ph.D. theses of – among others – Alfred Rosenblatt (1880-1947), Wacław Sierpiński (1882-1969), Włodzimierz Stożek (1883-1941) and Stanisław Gołąb (1902-1980) who considered himself also as – at least partially – a pupil of Hoborski and was continuing and developing research in differential geometry following Hoborski’s works in this domain. One of the outstanding pupils of Stanisław Zaremba (and later on, his successor) was Tadeusz Ważewski (1896-1972) who received his Ph.D. in 1923 in Paris and habilitation in 1927 in Kraków.

     Three strong scientific schools were created by mentioned above pupils of Zaremba and Żorawski. Franciszek Leja built up the well known school of analytic (complex) functions, Tadeusz Ważewski created the school of differential equations (called often by specialists : the Kraków School of Differential Equations), Stanisław Gołąb founded the known school of differential geometry and gave a basis for the school of functional equations developed afterwords by his pupils.

      Kazimierz Żorawski moved in autumn  of 1918 to Warsaw . However, before that, on the 2nd of April 1919 , he had chaired the inaugural meeting of the Mathematical Society which was born on that day in Kraków, becoming soon, after changing its name, the Polish Mathematical Society; among names of founders of the Society noted in the minutes (protocol) of this first meeting we can find the name of Stefan Banach (at that time the co-author of two papers written together with Hugo Steinhaus), who later lived in Lwów.  Stanisław Zaremba had been elected as the first President of the Society.  In that way the first and the most important period of building up the mathematical centre in Kraków by two outstanding professors acting at the turn of the century has been finished. Next years were characterised  by intensive and fruitful activity of Kraków mathematicians lead by Stanisław Zaremba developing first of all several areas of classical analysis in a large meaning of this term, also some parts of geometry and – in slightly smaller scale - other fields. Zaremba played very important and crucial role in building up new Polish mathematics which was expanding in three significant centres : Kraków, Warsaw and Lwów, and after the end of World War I entered a golden age . Further important progress measured by successes of three Kraków scientific schools mentioned above will take place after the World War II. However, some (few but essential) elements of bases of this progress were made during the war, when the Jagiellonian University was acting as an underground university (being formally closed by nazi occupants since November 1939); for instance certain important results of Tadeusz Ważewski were obtained by him during the war, after his return from the Sachsenhausen concentration camp in 1940). One can say, and it will be entirely correct, that the academic society was in that way fighting – without arms - against the occupants. Grey-headed  Stanisław Zaremba, however, didn’t live to the end of the war.     


     2. An outline of the curriculum vitae of Stanisław Zaremba.

     Stanisław Zaremba was born on the 3rd of September 1863 in a village Romanówka (now Ukraine). After completing his secondary education (in a high school in St.Ptersburg) he begun his studies in the Technological Institute in St.Petersburg and graduated from it in 1881 when he got a diploma of an engineer. Next step in his education was done in France where he studied mathematics getting – as it was mentioned above -  Ph.D. in Paris in 1889. Then he was teaching mathematics in secondary (high) schools in Digne, Nîmes and Cahors. In this period he collaborated with Paul Painlevé and Eduard Goursat.

     In 1900 he came to Kraków being nominated so-called extraordinary professor[1]. He became the ordinary professor (full professor) in 1905. His first university lecture had been delivered on 22nd of October 1900 on the notions of  limit and improper integral (see a relation of Antoni Hoborski, at that time a student of mathematics,  mentioned already in the first section above; [5], p.35). Zaremba served as the Dean of the Faculty of Philosophy of the Jagiellonian University during an extremely difficult academic year 1914/1915 at the beginning of the World War I. In 1903 he was elected as a “correspondent member” of the Academy of Sciences of Kraków[2] and in 1926 the full (“active”) member of it (at that time Polish Academy of Sciences and Arts). Zaremba got doctorate honoris causa of the Jagiellonian University in Kraków in 1930, University of Caen (France) in 1932, University in Poznań in 1934. The Jagiellonian University offered him in 1935 (at that time Zaremba was professor emeritus) the  title of  the honorary professor, very unusual dignity title. Stanisław Zaremba was a member of  the Russian Academy of Sciences (in Leningrad), Lwów Scientific Society, Royal Czech Scientific Society (elected in 1910), Poznań Society of Friends of Sciences (Poznańskie Towarzystwo Przyjaciół Nauk) and a honorary member of  “La Societé des Sciences, Agriculture et Arts des Bas-Rhin” in Strasbourg (elected in 1920).  Zaremba was  active in the Polish Mathematical Society (Polskie Towarzystwo Matematyczne); as it was mentioned already, he was the first President, but his activity was longer, larger and deeper than only one cadency of the presidency. Now, one of scientific prizes of the Society, so-called “great prizes” is named “Zaremba prize” (for further details we refer for instance to [4],[10],[11], [12], [13],[16]).

     The ceremony of granting Zaremba the doctorate honoris causa of the Jagiellonian University on 1st of February 1930 was an occasion to express a special tribute to him by several outstanding scientists present in Kraków or sending congratulation. The list of them contains in particular the following names : Stefan Banach, Wilhelm Blaschke, Émile Borel, Georges Bouligand, Élie Cartan, Arnoud Denjoy, Maurice Fréchet, Guido Fubini, Jaques Hadamard, Bronisław Knaster, Henri Lebesgue, Beppo Levi, Tullio Levi-Civitá, Léon Lichtenstein, Franciszek Leja, Jan Łukasiewicz, Stefan Mazurkiewicz, Paul Montel, Paul Painlevé, Giuseppe Peano, Émile Picard, Frédéric Riesz, Wacław Sierpiński, Hugo Steinhaus, Leonida Tonelli, Vito Volterra (compare [5]).


    3. Zaremba’s scientific output.

    Let us turn now our attention to Zaremba’s scientific output.  Presentation of it will be based on – first of all – the paper [22] written by Tadeusz Ważewski, an outstanding pupil of Stanisław Zaremba and Jacek Szarski, an outstanding pupil of Tadeusz Ważewski; we refer also to books and papers [4],[6],[8],[9],[10],[11],[12],[13] and [16].  The most essential comments on the scientific contents and importance of Zaremba’s papers are presented below following the article [22], which will not be cited in every case when particular paper or result is mentioned and commented.

     The main and general field of interest of Stanisław Zaremba was the theory of partial differential equations, especially of those coming from so called mathematical physics and several applications (in particular, but not only, applications in physics).

      The topic of the Ph.D. thesis of Zaremba has been already described above. Among his important results there are those concerning the elliptic equation

(1)                                                                                           u + u + f = 0

with boundary Dirichlet conditions as well as Neumann and Fourier type conditions. Some of these results were included into the canon of the fundamental knowledge on the theory of partial differential equations. Before talking about some details let us quote a sentence from the book [8] of Jean Mawhin : According to Bouligand[3]  Zaremba’s contribution to the development of the theory of  the Dirichlet problem is the same as that of Poincaré and Lebesgue.[4]

        In the paper [27] properties of the Green function G for a Dirichlet problem in the three dimensional space is considered and it is shown that the function

                                                      u = ds. 

is a solution to a given Dirichlet problem with the boundary condition described by a continuous function ; a discussion of properties of  u in the case of non-continuous is included as well.

       In the paper [28] Zaremba discussed the equation (1) for  f = 0 with the condition

(2)                                                                                               = hu

where h is a non-negative constant and  / is the interior normal derivative. He proved that there exist a sequence of eigenvalues and corresponding sequence {U} of orthonormal eigenfunctions. He proved also that if  is not an eigenvalue then the problem (1)-(2) (with  f=0)  has exactly one solution. Moreover, every function satisfying the boundary condition (2) can be represented as a Fourier series with respect to the sequence {U}  of eigenfunctions. Zaremba developed some idea of Poincaré and used generalised potentials defined by replacing in the classical definition of Newtonian potential the function 1/r  by the function exp(-r)/r  where    is a complex number such that    re  > 0   and    +  = 1. This notion of generalised potentials introduced by Zaremba turned out to be very useful in several other problems.

       Analogous results for the homogenous problem : (1) with  f=0  and the boundary problem u=0 are given in the paper [29].

      In [30] Zaremba gave some conditions sufficient for derivatives of arbitrary order of  solutions of  Dirichlet problems for the homogenous equation (1) (with  f=0) in a domain D to be continuous in the closure of D. Importance of this result is underlined by Jean Mawhin in the preface to the Polish version of his book [8].

        The paper [31] deals with the following problem. Let D be a bounded domain in the three dimensional real space, S be the intersections of the boundaries of  D and  -D,  n  the normal unit vector directed into the domain D.  For a function u of three real variables and a given point  x S   we put              

                                    ()=  lim (u(x+tn)-u(x))    as     

                               ()=  lim (u(x+tn)-u(x))    as      

and for a function  v  and   x S

           as     ,       and       as    ,  .

      We look for two solutions  u  and  v  of the homogenous equation  (1)  (that is with  f=0),  which are generalised potentials of  single layer and of double layer respectively, such that

                                 λ[] +   ,

                                        = λ[(v)+(v)] +

where λ is a parameter and  φ  is a given function defined on  S. Zaremba proved that this problem has (under general, relatively weak regularity assumptions) a solution which is an analytic function of   λ  and has at most one essential singularity (at infinity) and  single poles at points belonging to sequence of  real numbers independent on the function  φ. This permits to deal with the Neumann method assuming weak regularity conditions. An analogous problem on the plane is considered in the paper [32] (without the assumption of the continuity of  ). 

       In an earlier paper [26] Zaremba deals with successive approximations for solutions of a non-linear equation


This paper, as well as the paper [25], is cited in [14] (p.528) where a canon of the theory of elliptic partial differential equations is presented.

       The paper [41] is an extension of an unpublished note presented to the Paris Academy of Sciences and characterised by that Academy as extrémement honorable. A biharmonic problem considered there is such that we are looking for a solution   u   of the equation


considered in a domain  D  such that 

                         u = φ        and           on the boundary of the domain D,

where  φ  is a sufficiently regular function defined on   (in particular the second power of the Laplacian of  φ  is assumed to be integrable) requesting certain natural regularity condition to be fulfilled by  u.  Zaremba proved that in order to solve that problem it is sufficient to find a function  v  harmonic in  D , such that  v is integrable and for every harmonic function  h  such that  h is integrable on  D  the following equality is satisfied


Zaremba proved theorems on existence and uniqueness of solutions to that problem. He proved also that this problem can be solved by determining the minimum of an integral on  D.

       Basing on some result of the paper [37] Witold Wilkosz (1891-1941) proved a theorem on analyticity of  harmonic functions (see [23]).

        The Dirichlet problem with non-continuous boundary conditions was treated in the paper [38]; the main result of this paper is the first one of that type.

        Several other papers were devoted to the theory of the Dirichlet problem (see for instance [40],[42], [44], [49]). In papers [42],[44],[49] Zaremba developed his beautiful and fruitful idea of solving instead of the original Dirichlet problem some other problem which has always solutions and which can be reduced to the Dirichlet problem if the last one has a solution. Paper [40] gives some numerical method of solving  Dirichlet problems and – in a sense – extends the idea of the paper [39] which will be referred to later on in another context.

The Dirichlet problem was also the subject of Zaremba presentation [43] during the IV-th International Congress of Mathematicians in Rome in 1908. In papers [42] and [43] Zaremba introduced generalised solutions into the direct method of variational calculus built up by Hilbert (see [8]). In [42] an example of a domain in which there is no solution of a linear Dirichlet problem; it was the first such example in the literature, as it is pointed out by Jean Mawhin in [8] and by Pierre Dugac, Beno Eckman, Jean Mawhin and Jean-Paul Pier in the section “Guidelines 1900-1950” (see [3], p.6) presenting a list of the most important results obtained in this period the paper [42] is cited in the bibliography. In the same place ([3], p.6) Zaremba is mentioned as the author of a method of orthogonal projection in Dirichlet problem.

        In the paper [45] an equation of so-called spherical wave is considered. There is given a method of estimation of

where  u  is a solution of that equation. The idea of Zaremba used in his method was applied later on by Friedrichs and Levy in order to get known (now) integral inequalities satisfied by general solution of hyperbolic equations. These inequalities have been generalised by Juliusz Schauder (and became some fundamental elements in the survey of the theory of hyperbolic equations).

     Zaremba considered also several other problems. He discussed for example, as it has been mentioned already,  problems of Neumann and Fourier. An important contribution to the theory of Fourier problem was presented in [36].

      The Fourier equation                                    

                                             u - = 0              ( u=u(x,t) )

was the subject of Zaremba’s presentation (see [46]) during the International Congress of Mathematicians in Strasbourg in 1920[5]. 

     Let us now present some special part of  Zaremba’s contribution to the development of the theory of reproducing kernels (see for instance [15]). The best and probably the shortest way to do it is by referring to the Aronszajn paper [1]. He wrote : Examples of kernels of the type in which we are interested have been known for a long time, since all the Green’s functions of self-adjoint ordinary differential equations (as also some Green’s functions – the bounded ones – of partial differential equations) belong to this type (…) There have been and continue to be two trends in the consideration of these kernels (…). The second trend was initiated during the first decade of the century in the work of S.Zaremba [1,2][6] on boundary value problems for harmonic and biharmonic functions. Zaremba was the first to introduce, in a particular case, the kernel corresponding to a class of functions, and to state its reproducing property(…). However, he did not develop any general theory, nor did give any particular name to the kernels he introduced.  In that way one links certain results of Zaremba with some important part of the modern theory of operators which shows how deep were those result being now more than ninety years old.

      Stanisław Zaremba was interested in many problems of theoretical physics. His contribution to it was important. Let us mention some of his papers concerning theoretical physics, as for instance [33], [34], [35], [47], [48], [50]. Some comments on the paper [47] seems to be appropriate.  Zaremba criticised some ways of justification the relativity theory by experiments mentioned at that time as arguments for it. He didn’t find any mistake in this theory considered as an “abstract theory”, but he was not ready to agree with its consequences, especially in view of questioned value of discussed experiments. Let us add that Zaremba got later on a certain result concerning the relativity theory (for details see papers [18], [19], [20] by Bronisław Średniawa). In [19] there are some comments on the Zaremba’s  papers concerning electrodynamics; Średniawa pointed out that statements of Zaremba are correct from the mathematical point of view and methods used there are interesting but conclusions are improper for physics since instead of Lorentz transformation (with respect to which the Maxwell equations are invariant) the Galileo transformation had been used.

      Interesting particular questions belonging to theoretical physics (as for instance visco-elasticity and relaxation) were subjects of vigorous polemics between Zaremba and well known, outstanding physicist, professor of the Jagiellonian University, Władysław Natanson. They had different opinions on the degree of accuracy, permissibility of approximations and interpretation of results as well (compare for instance [33], [34], [35]). It is impossible to discuss here all details of that fascinating scientific polemics. One information might be, however, so interesting that it should be mentioned here. When a long sequence of notes and articles of Zaremba and Natanson was continuously published in the Bulletin Internationale de l’Académie de Sciences de Cracovie (Classe de Sciences Mathématiques et Naturelles) the editorial board, probably slightly irritated, included to the March 1904 issue of the Bulletin a short notice with the following text :La Classe des Sciences mathématiques et naturelles de l’Académie de Cracovie a decidé de ne publier, dans son Bulletin aucun nouvel article relatif à la polémique qui s’est angagée entre M.Natanson et M.Zaremba.  It should be added that one of the specific problem discussed by these two outstanding scientists was a generalisation (extension to the three dimensional case) of the one dimensional, Maxwell theory of visco-elasticity. The generalisation done by Natanson was criticised by Zaremba. According to C.Truesdell and W.Noll, authors of the article on the non-linear field theories of mechanics included in the Encyclopaedia of Physics (see [21]), Zaremba was right, while it has not been acknowledged in the literature in a proper way; they wrote : While the decision of time has been wholly for Zaremba, it has come late, and the vast literature on “plasticity” ignores it ([21], p.47). Trying to summarise in a brief form the Zaremba’s contribution to the theory of visco-elasticy (to the study of viscoelastic materials) one should say that results were really important. In particular he applied tensorial technics in this theory and proposed some precise definitions.

     The Encyclopaedia mentioned above uses the name the Zaremba-Jaumann form of the principle of material frame-indifference for the principle of invariantness of a fundamental equation of the theory, patterned upon the Maxwell equation of the kinetic gas theory.

      Stanisław Zaremba made an essential and effective effort on the way of axiomatic justification of the notion of time in classical mechanics (which was the main subject of his work during the last period of his scientific activity in Kraków, from 1933 to 1940). This joins two domains of his research : theoretical mechanics and logic; since among Zaremba’s fields of interest there was also mathematical logic. Besides purely scientific approach (and some publications) he was engaged in a polemic with certain mathematicians and logicians connected with scientific centres of  Warsaw and Lwów. The beginning of this polemic was related to the definition of the notion of the value (wielkość in Polish), but soon the question of the  degree of formal strictness in mathematical resoning needed in research papers and in the textbooks as well became the main subject of a vigorous discussion. Interesting comments on this aspect of scientific activity of Zaremba can be found in the book [24] where several other fields of discussions and polemics undertaken by members of Polish scientific centres are presented in a large context.

       It was pointed out that Stanisław Zaremba was interested very much in several applications of mathematics. One more example of his engagement in building up links between mathematics and applications can be indicated by an information on his research, common with a professor of mineralogy Stefan Kreutz, concerning the crystallography. They proposed a precise formal definition of a notion called : crystallography system (we refer to [22] for more information and some comments).

      It should be added finally that Zaremba wrote several valuable textbooks on analysis and theoretical mechanics (seemed to be the most important) and on selected topics of linear algebra was well.

       The authors of the paper [22] (to which we have referred here several times) quote a significant phrase of Henri Lebesgue who said that Stanisław Zaremba never wrote a needless paper. It is difficult to imagine more laudatory opinion on scientific activity of anybody.

        Concluding this essay let us quote Kazimierz Kuratowski [6] who expressed his view on the Zaremba life and work :  Stanisław Zaremba is the pride of Polish science.




 [1]  N.Aronszajn, Theory of reproducing kernels, Trans. Amer. Mat. Soc.,68(1950), 337-404.     

 [2] G.Bouligand, Fonctions harmoniques. Principes de Picard et Dirichlet. Memorial de Sciences Math., Paris, fasc.XI, Gauthier-Villars, 1926.

 [3]  Development of Mathematics 1900-1950, edited by Jean-Paul Pier, Birkhäuser Verlag, Basel-Boston-Berlin,1994.

 [4]  S.Gołąb, Zarys dziejów matematyki na Uniwersytecie Jagiellońskim w XX wieku (An outline of the history of mathematics at the Jagiellonian University in XX-th century [in Polish]), [in:] Studia z dziejów katedr Wydziału Matematyki, Fizyki, Chemii Uniwersytetu Jagiellońskiego, S.Gołąb ed., Kraków 1964, 75-86.

 [5]  Jubilé scientifique de M.Stanislas Zaremba (1 février 1930) (publié par le soins du comité), Cracovie 1930.

 [6] K.Kuratowski, Pół wieku matematyki polskiej 1920-1970,  (Half century of  Polish mathematics [in Polish]), Warszawa 1973.

 [7] O.Lehto, Mathematics Without Borders, Springer-Verlag New York, Inc, 1998.

 [8]  J.Mawhin, Metody wariacyjne dla nieliniowych problemów Dirichleta, (Polish version of the book Problèmes de Dirichlet variationneles non linéaires; translated by D.P.Idziak, A.Nowakowski, S.Walczak), Warszawa 1995. 

 [9] Z.Opial, Zarys dziejów matematyki na Uniwersytecie Jagiellońskim w drugiej połowie XIX wieku  (An outline of the history of mathematics at the Jagiellonian University in the second half of the XIX-th century [in Polish]) [in:] Studia z dziejów katedr Wydziału Matematyki, Fizyki, Chemii Uniwersytetu Jagiellońskiego, S.Gołąb ed., Kraków 1964, 59-74.

[10] Z.Pawlikowska-Brożek, S.Kolankowski, Zaremba Stanisław /1863-1942/ [in Polish], [in:] Materiały dotyczące Słownika Biograficznego Matematyków Polskich, Institute of Mathematics of the Polish Academy of  Sciences, Preprint C-3 (without the date of publication), 120-123.

[11] A.Pelczar, Matematyka w Polsce u początków PTM (i nieco wcześniej) (Mathematics in Poland at the beginning of the Polish Mathematical Society (and slightly earlier) [in Polish]), Wiadomości Matematyczne, 32(1996), 137-152.

[12]  A.Pelczar, Kazimierz Paulin Żorawski i Stanisław Zaremba (Kazimierz Paulin Żorawski and Stanisław Zaremba [in Polish]) [in:] Złota Księga Wydziału Matematyki i Fizyki Uniwersytetu Jagiellońskiego, Kraków 2000,313-327.

[13]  A.Pelczar, On a functional-differential equation (in a historical context), Opuscula Mathematica, 19(1999),45-61.

[14]  A.Sommerfeld, Randwertaufgaben in der Theorie der partiellen Differentialgleichungen, [in:] Ecyklopädie der Mathematischen Wissenschaften,band II-1, Leipzig 1907, 505-570.

[15]  F.H.Szafraniec, The reproducing kernel Hilbert space and its multiplication operators, Operator Theory: Advances and Applications, 114(2000),253-263.

[16] J.Szarski, Stanisław Zaremba (1863-1942) [in Polish], Wiadomości Matematyczne, 5(1962),15-28.

[--]  J.Szarski, T.Ważewski – see : [22], T.Ważewski, J.Szarski.

[17]  W.Ślebodziński, Kazimierz Żorawski [in Polish], [in:] Studia z dziejów katedr Wydziału Matematyki, Fizyki, Chemii Uniwersytetu Jagiellońskiego, S.Gołąb ed.,Kraków 1964, 87-101. [18]  B.Średniawa, History of Theoretical Physics at Jagiellonian University in Cracow in XIXth Century and in the First Half of XXth Century, Zeszyty Naukowe Uniwersytetu Jagiellońskiego, Prace Fizyczne,24(1985).

[19] B.Średniawa, Współpraca matematyków, fizyków i astronomów w Uniwersytecie Jagiellońskim w XIX i pierwszej połowie XX wieku (Cooperation between mathematicians, physicists and astronomers at the Jagiellonian University in the XIX-th century and the first half of the XX-th century [in Polish])[in:] Studia z historii astronomii, fizyki i matematyki w Uniwersytecie Jagiellońskim, Zeszyty Naukowe UJ, Prace Fizyczne, 25(1986),53-82.

[20] B.Średniawa, Recepcja teorii względności w Polsce (Reception in Poland of the relativity theory [in Polish]), Kwartalnik Nauki i Techniki, 3-4(1985),555-584.

[21] C.Truesdell, W.Noll, The Non-Linear Field Theories of Mechanics [in:] Encyclopedia of Physics/Handbuch der Physik, S.Flüge ed.,vol.III, part 3, Springer Verlag, Berlin-Heidelberg-New York,1965.

[22] T.Ważewski, J.Szarski, Stanisław Zaremba [in Polish],[in:] Studia z dziejów katedr Wydziału Matematyki, Fizyki, Chemii Uniwersytetu Jagiellońskiego, S.Gołąb ed., Kraków 1964, 103-117.

[23]  W.Wilkosz, Sur un point fondamental de la théorie du potentiel, Comptes Rendus de l’Académie des Sciences de Cracovie, 174(1922), 435-437.

[24] J.Woleński, Szkoła lwowsko-warszawska w polemikach (Warsaw-Lwów school in polemics [in Polish]), Warszawa 1997.

[25]  S.Zaremba, Contribution a la théorie de la fonction de Green, Bulletin de la Société Mathématique de France, 54(1896), 19-24.

[26]  S.Zaremba, Sur la méthode d’approximations successives de M.Picard, Journal de Mathématiques pures et appliquées, (5),3 (1897), 311-329.

[27]  S.Zaremba, Sur le problème de Dirichlet, Annales de l’École Normale(3),14(1897),251-258.

[28]  S.Zaremba, Sur l’équation aux dérivées partielles u + ξu + f = 0 et sur les fonctions harmoniques, Annales de l’École Normale,(3)16(1899),427-463.

[29]  S.Zaremba, Sur le développement d’une fonction arbitraire en un série procédant suivant les fonctions harmoniques, Journal de Mathématiques pures et appliquées,(5),6(1900),47-72.

[30]  S.Zaremba, Contribution à la théorie de l’équation aux dérivées partielles , Annales de la Faculté des Sciences d l’Université de Toulouse, (32),3(1900),5-12.

[31]  S.Zaremba, Sur l’intégration de l’équation , Journal de Mathématiques pures et appliqueés, (5),8(1902),59-117.

[32]  S.Zaremba, Les fonctions fondamentales de M.Poincaré et la méthode de Naumann pour une frontière composée des polygones curvilignes, Journal de Mathématiques pures et appliquées, (5),10(1904), 395-444.

[33] S.Zaremba, Sur un problème d’hydrodynamique lié à un cas de double réfraction accidentelle dans les liquides et sur les considération théoreques de W.Natanson relatives à ce phénomène, Bulletin International de l’Académie des Sciences de Cracovie, 1903, 404-422.

[34] S.Zaremba, Sur une généralisation de la théorie classique de la viscosité, Bulletin International de l’Académie des Sciences de Cracovie, Classe des Sciences Mathématiques et Naturelles, 1903,381-403.

[35] S.Zaremba,  Sur une forme perfectionnée de la théorie de la relaxation, Bulletin International de l’Académie des Sciences de Cracovie, Classe des Sciences Mathématiques et Naturelles, 1903, 595-614.

[36]  S.Zaremba, Solution générale du problème de Fourier, Bulletin International de l’Académie des Sciences, Classe des Sciences Mathématiques et Naturelles, 1905, 69-168.

[37] S.Zaremba, Contribution à la théorie d’une équation fonctionelle de la physique, Rendiconti del Circolo Matematico di Palermo, 19(1904),140-150.

[38]  S.Zaremba, Sur l’unicité de la solution du problème de Dirichlet, Bulletin International de l’Académie des Sciences de Cracovie, Classe des Sciences Mathématiques et Naturelles, 1909,561-564.

[39] S.Zaremba, L’équation biharmonique et une classe remarquable de fonctions fonda-mentales harmoniques, Bulletin International de l’Académie des Sciences de Cracovie, Classe des Sciences Mathématiques et Naturelles, 1907, (3), 147-196.

[40] S.Zaremba, Sur le calcul numérique des fonctions demandées dans le problème de Dirichlet et le problème hydrodynamique, Bulletin International de l’Académie des Sciences de Cracovie, Classe des Sciences Mathématiques et Naturelles, 1909,(2),125-195.

[41] S.Zaremba, Le problème biharmonique restreint, Annales de l’École Normale, (3),26 (1909),337-404.

[42] S.Zaremba, Sur le principe du minimum, Bulletin Internationale de l’Académie des Sciences de Cracovie, Classe des Sciences Mathématiques et Naturelles, 1909,(7),197-264.

[43] S.Zaremba, Sur le principe de Dirichlet, Atti del IV Congresso Internazionale dei Matematici (Roma, 6-11 Aprile 1908), vol.II, Communicazioni delle sezioni I e II, Roa 1909, 194-199.

[44]  S.Zaremba, Sur le principe de Dirichlet, Acta Mathematica,34(1911),293-316.

[45]  S.Zaremba, Sopra un teorema d’unicita relativo alla equazione della onde sferiche, R.C. della Accademia dei Lincei, (5),24(1915),904-908.

[46]  S.Zaremba, Sur un théoreme fondamental relatif à l’èquation de Fourier, Compte Rendus du Congrés International des Mathématiciens (Strasbourg 22-30 Septembre 1920), Toulouse 1921,  343-350.

[47] S.Zaremba La théorie de la relativité et les faits observés, Journal de Mathématiques pures et appliquées, (9),1(1922),105-139.

[48] S.Zaremba, Sur un groupe de transformation qui se présentent en électrodynamique, Annales de la Société Polonaise de Mathématiques, 5(1926),3-19.

[49]  S.Zaremba, Sur un problème toujours possible comprenant à titre de cas particuliers, le problème de Dirichlet et celui de Neumann, Journal de Mathématiques pures et appliquées,(9),6(1927),127-163.

[50]   S.Zaremba,   Sur  le   changement  du  système  de  référence  pour  un  champ   électro-  

magnétique déterminé, Annales de la Société Mathématiques, 6(1927),8-49.





Prepared for the   International Conference  90  years  of  the reproducing  Kernel  Property,

Kraków, April 16-21, 2000 organised by the Chair of Functional Analysis of the Jagiellonian University.





 Kraków, April 12, 2000.               

[1] According to the Polish university tradition there are two professorship positions : extraordinary professor (practically equivalent ot the position of associate professor in USA) and ordinary professor (full professor).

[2] Academy of Sciences , in Polish :  Akademia Umiejętności (the Polish name can be translated also as the Academy of Sciences and Arts, since the word „umiejętność” is not equivalent to the word „science”) established i 1872 (started its real activity in 1873), became in 1919 the Polish Academy of Sciences and Arts (Polska Akademia Umiejętności - PAU). Its activity was interrupted in 1952, reactivated in 1989. It is acting now independently on the Polish Academy of Sciences (Polska Akademia Nauk – PAN) established in 1952. There are two categories of members of PAU : „correspondent” and „active” (=ordinary, full).

[3] Here the paper [2] is referred.

[4] A translation of the Polish fraze : Zdaniem Bouliganda wkład Zaremby w rozwój teorii problemu Dirichleta  jest taki sam jak Poincarégo i Lebesgue’a.

[5] Let us recall that the International Mathematical Union (IMU) was founded at that time. As the exact date one should indicate: 20 September 1920 (compare Olli Lechto [7]).  Countries-founders were: Belgium, Czechoslovakia, France, Greece, Italy, Japan, Poland, Portugal, Serbia, United Kindom, United States. Zaremba was the Polish representative. Zaremba was involved once again in the activity of IMU being appointed as a member of a Commission to study the question of permanent international collaboration in mathematics formed  by the President of the 1932 International Congress of Mathematiciens (Zürich) according to the decision and authorisation of the General Assembly of IMU. After consultation with E.Cartan, Severi,Veblen and Weyl, he appointed  - as we read in [7] (p.58) - F.Severi (Rome) as Chairman of the Commissio and the following members : P.S.Aleksandrov (Moscow), H.Bohr (Copenhagen), L.Fejér (Budapest), G.Julia (Paris),L.J.Mordell (Manchester), E.Terradas (Madrid), la Vallée Poussin (Louvai), O.Veblen (Princeton), H.Weyl (Göttingen) and S.Zaremba (Cracow).

[6] That is the papers [39] and [40] in the list of the present article