Salomon Bochner

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Salomon Bochner (20 August 1899 - 2 May 1982) was a Polish-American mathematician, known for wide-ranging work in mathematical analysis, probability theory and differential geometry. He was born into a Jewish Family in Podgórze (near Kraków), Poland. Studied at the University of Warsaw. Fearful of a Russian invasion in Poland 1914, he moved in 1915 to Germany, seeking greater security. Bochner was educated at a Berlin gymnasium (secondary) school, and then at the University of Berlin. There, he was a student of Erhard Schmidt, writing a dissertation involving what would later be called the Bergman kernel. His academic career in Germany came to an end in 1933, and he left for a position at Princeton University. He died in Houston, Texas.

In 1925 he started work in the area of almost periodic functions, simplifying the approach of Harald Bohr by use of compactness and approximate identity arguments. In 1933 he defined the Bochner integral, as it is now called, for vector-valued functions. Bochner's theorem on Fourier transforms appeared in a 1932 book. His techniques came into their own as Pontryagin duality and then the representation theory of locally compact groups were development in the following years.

Subsequently he worked on multiple Fourier series, posing the question of the Bochner-Riesz means. This led to results on how the Fourier transform on Euclidean space behaves under rotations.

In differential geometry, Bochner's formula on curvature from 1946 was most influential. Joint work with Kentaro Yano (1912-1993) led to the 1953 book Curvature and Betti Numbers. It had broad consequences, for the Kodaira vanishing theory, representation theory, and spin manifolds. Bochner also worked on several complex variables (the Bochner-Martinelli formula and the book Several Complex Variables from 1948 with W. T. Martin).

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