Salomon Bochner

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Salomon Bochner (born August 20, 1899 in Podgórze near Cracow , today Poland ; † May 2, 1982 in Houston , Texas ) was an American mathematician who worked in the field of analysis (e.g. harmonic analysis , almost periodic functions , several complex variables , differential geometry ) worked.

life and work

Bochner was born as the second child of an Orthodox Jewish family in what was then part of Austria-Hungary (near Krakow ). With the outbreak of World War I, the family moved to Berlin to face an impending Russian invasion . Bochner attended grammar school there and from 1918 the university. In 1921 he received his doctorate from Erhard Schmidt with a dissertation on orthogonal systems of analytical functions (the work already contained the Bergman kernel , named after Stefan Bergman , who was working in this field at the same time). In the subsequent inflationary times he supported his family with a successful foreign trade business, but then returned to mathematical research in 1923. He simplified the theory of almost periodic functions developed by Harald Bohr ( Niels Bohr's brother ) and was invited by Bohr to Copenhagen in 1924 .

He then also attended, on a scholarship, Godfrey Harold Hardy and John Edensor Littlewood at Cambridge University . From 1924 to 1933 he was at the University of Munich, where he completed his habilitation in 1927. During this time his lectures on Fourier integrals appeared , which among other things contained the Bochner theorem (every positive definite function is a Fourier transform of a positive finite Borel measure ). He wrote a paper in which he used the lemma of Zorn several years before Zorn and introduced the Bochner integrals . Attempts by his Munich colleagues Constantin Carathéodory and Oskar Perron to get him an assistant professorship initially failed, and a recommendation to Harvard University was unsuccessful because of resistance from George David Birkhoff .

With the seizure of power of the Nazis in 1933 his position became untenable and he went to the USA to Princeton , where he became assistant professor in 1934. In 1938 he married (the marriage resulted in a daughter) and took US citizenship. In the same year he became an associate professor and then in 1946 a full professor at Princeton, where he remained until his retirement in 1968. But even after that he remained active and was then a professor at Rice University in Houston until his death . During his time in Princeton he worked with John von Neumann on almost periodic functions on groups and began his investigations into the functions of several complex variables, summarized in 1948 in the book Several complex variables with W. Martin (among other things he transferred Cauchy's integral formula in 1944 to the multi-dimensional case and proved the Bochner-Martinelli formula ), which has long been the standard work on this in the United States. Other areas of interest in his later years were differential geometry ( Bochner's formula of curvature 1946), probability theory and the history of science.

In 1950 he was elected to the National Academy of Sciences . 1957/58 he was president of the American Mathematical Society . In 1979 he received the Leroy P. Steele Prize from the American Mathematical Society. In 1950 he gave a plenary lecture at the International Congress of Mathematicians in Cambridge , Massachusetts on Laplace Operator on Manifolds .

His doctoral students include Lynn Loomis , Harry Rauch , Anthony W. Knapp , Hillel Fürstenberg , William Veech , Samuel Karlin , Eugenio Calabi , Sigurdur Helgason , Robert Gunning , Richard Askey , Jeff Cheeger .

Works

See also

  • Bochner's theorem , characterization of characteristic functions in probability theory.

Web links

personal data
SURNAME Bochner, Salomon
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH August 20, 1899
PLACE OF BIRTH Podgórze near Krakow , Austria-Hungary (today: Poland )
DATE OF DEATH May 2, 1982
Place of death Houston , Texas , United States