- Salomon Bochner
Infobox Scientist
name = Salomon Bochner
field =Mathematics
alma_mater =University of Berlin
doctoral_advisor =Erhard Schmidt
doctoral_students =Richard Askey Jeff Cheeger Hillel Furstenberg Israel Halperin
known_for =Bochner integral Bochner's theorem Salomon Bochner (
20 August 1899 –2 May 1982 ) was an Americanmathematician of Austrian-Hungarian origin, known for wide-ranging work inmathematical analysis ,probability theory anddifferential geometry .Life
He was born into a Jewish Family in Podgórze (near
Kraków ), then Austria-Hungary, nowPoland . He studied at theUniversity of Warsaw . Fearful of a Russian invasion in Galicia at the beginning ofWorld War I in 1914, his family moved toGermany , seeking greater security. Bochner was educated at aBerlin gymnasium (secondary school), and then at theUniversity of Berlin . There, he was a student ofErhard Schmidt , writing a dissertation involving what would later be called theBergman 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 University of Munich from 1924 to 1933. His academic career in Germany ended after the Nazis came to power in 1933, and he left for a position atPrinceton University . He died inHouston, Texas . He was anOrthodox Jew . [ [http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Bochner.html Bochner biography ] ]Mathematical work
In 1925 he started work in the area of
almost periodic function s, simplifying the approach ofHarald Bohr by use ofcompactness andapproximate identity arguments. In 1933 he defined theBochner integral , as it is now called, for vector-valued functions.Bochner's theorem onFourier transform s appeared in a 1932 book. His techniques came into their own asPontryagin duality and then the representation theory oflocally compact group s developed in the following years.Subsequently he worked on
multiple Fourier series , posing the question of theBochner-Riesz mean s. This led to results on how the Fourier transform onEuclidean space behaves under rotations.In differential geometry,
Bochner's formula oncurvature 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 theKodaira vanishing theory ,representation theory , andspin manifold s. Bochner also worked onseveral complex variable s (theBochner-Martinelli formula and the book "Several Complex Variables" from 1948 withW. T. Martin ).See also
*
Bochner identity
*Bochner space econdary literature
* Cooke, Roger, 2005, "Lectures on
Fourier integral s" in Grattan-Guinness, I., ed., "Landmark Writings in Western Mathematics". Elsevier: 945-59.References
External links
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