Salomon Bochner

Salomon Bochner (20 August 1899 – 2 May 1982) was a Galizien-born mathematician, known for work in mathematical analysis, probability theory and differential geometry.

Life He was born into a Jewish family in Podgórze (near Kraków), then Austria-Hungary, now Poland. Fearful of a Russian invasion in Galicia at the beginning of World War I in 1914, his family moved to Germany, seeking greater security. Bochner was educated at a Berlin gymnasium (secondary school), and then at the Friedrich Wilhelm University of Berlin. There, he was a student of Erhard Schmidt, He was appointed as Henry Burchard Fine Professor in 1959, retiring in 1968. Although he was seventy years old when he retired from Princeton, Bochner was appointed as Edgar Odell Lovett Professor of Mathematics at Rice University and went on to hold this chair until his death in 1982. He became Head of the Department at Rice in 1969 and held this position until 1976. He died in Houston, Texas. He was an Orthodox Jew.

Mathematical work 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 developed 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 was published in 1946. Joint work with Kentaro Yano (1912–1993) led to the 1953 book Curvature and Betti Numbers. It had consequences for the Kodaira vanishing theory, representation theory, and spin manifolds. Bochner also worked on functions of several complex variables, resulting in the Bochner–Martinelli formula and the book Several Complex Variables (with W. T. Martin in 1948).

Selected publications

Lectures given in 1937-1938, notes by J. W. Tukey, J. Giese, and V. Martin.

2016 reprint

2013 reprint 2014 reprint