Juliusz Schauder
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Juliusz Paweł Schauder (1899-1943) was a Polish mathematician.
Born on September 21 1899 in Lwów, he had to fight in World War I right after his graduation from school. He was captured and imprisoned in Italy. 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. After the beginning of World War II he was finally appointed professor in Lwów.
Schauder was Jewish, and after the invasion of German troops in Lwów it was impossible for him to continue his work - it was even impossible for him to write down his last results, for lack of paper. He was murdered by the Gestapo, probably in September 1943.
Most of his mathematical work belongs to the field of functional analysis, being part of a large Polish group of mathematicians (e.g., Banach, Borsuk, Orlicz, Sierpinski, Steinhaus, Ulam) of pioneers in this area with wide applications in all parts of modern analysis. He is best known for the Schauder fixed point theorem which is a major tool to prove the existence of solutions in various problems. Other concepts introduced by him include the notion of Schauder bases (the generalization of a orthonormal basis from Hilbert spaces to Banach spaces) and the Leray-Schauder principle, a way to establish solutions of partial differential equations from a priori estimates.de:Juliusz Schauder