Juliusz Paweł Schauder (; 21 September 1899,
Lwów,
Austria-Hungary
Austria-Hungary, often referred to as the Austro-Hungarian Empire,, the Dual Monarchy, or Austria, was a constitutional monarchy and great power in Central Europe between 1867 and 1918. It was formed with the Austro-Hungarian Compromise of ...
– September 1943, Lwów,
Occupied Poland
' ( Norwegian: ') is a Norwegian political thriller TV series that premiered on TV2 on 5 October 2015. Based on an original idea by Jo Nesbø, the series is co-created with Karianne Lund and Erik Skjoldbjærg. Season 2 premiered on 10 Octobe ...
) was a Polish
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
of
Jewish
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
origin, known for his work in
functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...
,
partial differential equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function.
The function is often thought of as an "unknown" to be solved for, similarly to ...
and
mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developme ...
.
Life and career
Born on 21 September 1899 in Lwów, he was drafted into the
Austro-Hungarian Army
The Austro-Hungarian Army (, literally "Ground Forces of the Austro-Hungarians"; , literally "Imperial and Royal Army") was the ground force of the Austro-Hungarian Dual Monarchy from 1867 to 1918. It was composed of three parts: the joint arm ...
right after his graduation from school and saw action on the
Italian front. He was captured and imprisoned in
Italy
Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical ...
. He entered the university in Lwów in 1919 and received his doctorate in 1923. He got no appointment at the university and continued his research while working as teacher at a secondary school. Due to his outstanding results, he obtained a scholarship in 1932 that allowed him to spend several years in Leipzig and, especially, Paris. In Paris he started a very successful collaboration with
Jean Leray
Jean Leray (; 7 November 1906 – 10 November 1998) was a French mathematician, who worked on both partial differential equations and algebraic topology.
Life and career
He was born in Chantenay-sur-Loire (today part of Nantes). He studied at Éc ...
. Around 1935 Schauder obtained the position of a senior assistant in the
University of Lwów
The University of Lviv ( uk, Львівський університет, Lvivskyi universytet; pl, Uniwersytet Lwowski; german: Universität Lemberg, briefly known as the ''Theresianum'' in the early 19th century), presently the Ivan Franko Na ...
. Schauder, along with
Stanisław Mazur
Stanisław Mieczysław Mazur (1 January 1905, Lwów – 5 November 1981, Warsaw) was a Polish mathematician and a member of the Polish Academy of Sciences.
Mazur made important contributions to geometrical methods in linear and nonlinear functio ...
, was an Invited Speaker of the
ICM in 1936 in Oslo.
Schauder was
Jewish
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
, and after the
invasion of German troops in Lwów 1941 it was impossible for him to continue his work. Even before the Lwów ghetto was established he wrote to
Ludwig Bieberbach
Ludwig Georg Elias Moses Bieberbach (; 4 December 1886 – 1 September 1982) was a German mathematician and Nazi.
Biography
Born in Goddelau, near Darmstadt, he studied at Heidelberg and under Felix Klein at Göttingen, receiving his doctorat ...
pleading for his support. Instead, Bieberbach passed his letter to the
Gestapo
The (), abbreviated Gestapo (; ), was the official secret police of Nazi Germany and in German-occupied Europe.
The force was created by Hermann Göring in 1933 by combining the various political police agencies of Prussia into one orga ...
and Schauder was arrested. In his letters to Swiss mathematicians, he wrote that he had important new results, but no paper to write them down. He was executed by the
Gestapo
The (), abbreviated Gestapo (; ), was the official secret police of Nazi Germany and in German-occupied Europe.
The force was created by Hermann Göring in 1933 by combining the various political police agencies of Prussia into one orga ...
, probably in October 1943.
Most of his mathematical work is in the field of
functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...
, being part of a large Polish group of mathematicians, i.e.
Lwów School of Mathematics
The Lwów school of mathematics ( pl, lwowska szkoła matematyczna) was a group of Polish mathematicians who worked in the interwar period in Lwów, Poland (since 1945 Lviv, Ukraine). The mathematicians often met at the famous Scottish Café to ...
. They were pioneers in this area with wide applications in all parts of modern analysis. Schauder is best known for the
Schauder fixed-point theorem The Schauder fixed-point theorem is an extension of the Brouwer fixed-point theorem to topological vector spaces, which may be of infinite dimension. It asserts that if K is a nonempty convex closed subset of a Hausdorff topological vector space V ...
which is a major tool to prove the existence of solutions in various problems, the
Schauder bases (a generalization of an
orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space ''V'' with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For examp ...
from
Hilbert spaces to
Banach spaces), and the
Leray−Schauder principle, a way to establish solutions of
partial differential equations from
a priori estimates.
In memoriam
The Schauder Medal
is awarded by the J.P. Schauder Center for Nonlinear Studies at the
Nicolaus Copernicus University in Toruń
Nicolaus Copernicus University in Toruń or NCU ( pl, Uniwersytet Mikołaja Kopernika w Toruniu, UMK) is located in Toruń, Poland. It is named after Nicolaus Copernicus, who was born in Toruń in 1473.topological
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
methods in
nonlinear analysis
Nonlinear functional analysis is a branch of mathematical analysis that deals with nonlinear mappings.
Topics
Its subject matter includes:
* generalizations of calculus to Banach spaces
* implicit function theorems
* fixed-point theorems (Br ...
.
See also
*
Banach–Schauder theorem
In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental result which states that if a bounded or continuous linear opera ...
*
Schauder basis In mathematics, a Schauder basis or countable basis is similar to the usual ( Hamel) basis of a vector space; the difference is that Hamel bases use linear combinations that are finite sums, while for Schauder bases they may be infinite sums. This ...
*
Schauder estimates
*
Schauder fixed point theorem The Schauder fixed-point theorem is an extension of the Brouwer fixed-point theorem to topological vector spaces, which may be of infinite dimension. It asserts that if K is a nonempty convex closed subset of a Hausdorff topological vector space V ...
*
List of Polish mathematicians
A list of notable Polish mathematicians:
References
{{Reflist
Mathematicians
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concern ...
References
External links
*
*
*
Juliusz P. Schauder Center for Nonlinear Studies
{{DEFAULTSORT:Schauder, Juliusz
1899 births
1943 deaths
Academic staff of the University of Lviv
Jews from Galicia (Eastern Europe)
Lwów School of Mathematics
Blue Army (Poland) personnel
Polish Jews who died in the Holocaust
PDE theorists