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Juliusz Paweł Schauder (September 21, 1899–September 1943) was a Polishmarker mathematician of Jewish origin, known for his work in functional analysis, partial differential equation and mathematical physics.

Born on September 21 1899 in Lwówmarker, he had to fight in World War I right after his graduation from school. He was captured and imprisoned in Italymarker. 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. Around 1935 Schauder obtained the position of a senior assistant in the University of Lwów.

Schauder was Jewish, and after the invasion of German troops in Lwów it was impossible for him to continue his work. 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 Gestapomarker, probably in October 1943.

Most of his mathematical work belongs to the field of functional analysis, being part of a large Polish group of mathematicians, i.e. Lwów School of Mathematics. 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 which is a major tool to prove the existence of solutions in various problems, the Schauder bases (a generalization of an 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.

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