**(100 ^{th} 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 2^{nd} 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 3^{rd} 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 22^{nd} 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 1^{st} 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* +

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

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 _{}*

* *(_{})_{}=
*lim _{}*

and for a function *v *and
*x _{}_{} S*

_{} *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*[_{}] + *2φ* ,

_{}= *λ*[(*v*)_{}+(*v*)_{}] + *2φ*

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

_{}.

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 *

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.*

**References**

** **[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,

[40] __S.Zaremba__, Sur le calcul
numérique des fonctions demandées dans le problème de Dirichlet et le problème
hydrodynamique,

[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), Ch.de 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