Salomon Bochner

Salomon Bochner studied at Frederick William University Berlin. Chandrasekharan and Robert Langlands are recorded as having studied under Salomon Bochner. The recorded working language is German, English and French. The field of work recorded is mathematical analysis, probability theory and differential geometry. Places of work recorded in the authority are Berlin, Munich and Princeton. Employment is recorded with Princeton University, Rice University and Ludwig-Maximilians-Universität München. Works named in the authority record are Lectures on Fourier Integrals, Groups of Differentiable and Real or Complex Analytic Transformations, On Compact Solutions of Operational-Differential Equations. Distinctions recorded are Leroy P.

• Name — Salomon Bochner • Born — 20 August 1899 • Birthplace — Podgórze, Austria-Hungary • Died — 2 May 1982 • Place of death — Houston, Texas • Fields — Mathematics • Workplaces — Ludwig-Maximilians-Universität München Princeton University Institute for Advanced Study Rice University • Education — Friedrich Wilhelm University of Berlin • Doctoral Advisor — Erhard Schmidt • Doctoral Students — Richard Askey Eugenio Calabi Jeff Cheeger M. T. Cheng Charles L. Dolph Hillel Furstenberg Robert Gunning Israel Halperin Sigurdur Helgason Carl Herz Gilbert Hunt Samuel Karlin Anthony Knapp Paco Lagerstrom Lynn Loomis Harry Rauch Joseph H. Sampson Herbert Scarf William A. Veech Gerard Washnitzer Bernard Russell Gelbaum • Known for — Bochner's formula Bochner identity Bochner integral Bochner space Bochner's theorem Bochner's tube theorem Bochner–Martinelli formula Bochner–Minlos theorem Bochner–Riesz mean Bochner–Yano theorem Formal group law • Awards — AMS Steele Prize 1979

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, writing a dissertation involving what would later be called the Bergman kernel. Shortly after this, he left the academy to help his family during the escalating inflation. After returning to mathematical research, he lectured at the Ludwig-Maximilians-Universität München from 1924 to 1933. His academic career in Germany ended after the Nazis came to power in 1933, and he left for a position at Princeton University. He was a visiting scholar at the Institute for Advanced Study from 1945 to 1948. 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.

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).