Salomon Bochner | |
|---|---|
 circa 1970 | |
| Born | (1899-08-20)20 August 1899 |
| Died | 2 May 1982(1982-05-02) (aged 82) |
| Alma mater | University of Berlin |
| 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[1][2] |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Munich Princeton University Institute for Advanced Study Rice University |
| Doctoral advisor | Erhard Schmidt[3] |
| 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[4] |
Salomon Bochner (20 August 1899 – 2 May 1982) was aGalizien-bornmathematician, known for work inmathematical analysis,probability theory anddifferential geometry.
He was born into aJewish family inPodgórze (nearKraków), then Austria-Hungary, nowPoland. Fearful of a Russian invasion inGalicia at the beginning ofWorld War I in 1914, his family moved to Germany, seeking greater security. Bochner was educated at aBerlingymnasium (secondary school), and then at theUniversity of Berlin. There, he was a student ofErhard Schmidt,[3] writing a dissertation involving what would later be called theBergman kernel. Shortly after this, he left the academy to help his family during theescalating inflation[broken anchor]. After returning to mathematical research, he lectured at theUniversity of Munich from 1924 to 1933. His academic career in Germany ended after theNazis came to power in 1933, and he left for a position atPrinceton University. He was a visiting scholar at theInstitute for Advanced Study in 1945 to 1948.[5] 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 atRice University and went on to hold this chair until his death in 1982. He became Head of Department at Rice in 1969 and held this position until 1976. He died inHouston, Texas. He was anOrthodox Jew.[6]
In 1925 he started work in the area ofalmost periodic functions, 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 transforms appeared in a 1932 book. His techniques came into their own asPontryagin duality and then the representation theory oflocally compact groups developed in the following years.
Subsequently, he worked onmultiple Fourier series, posing the question of theBochner–Riesz means. This led to results on how the Fourier transform onEuclidean space behaves under rotations.
In differential geometry,Bochner's formula oncurvature from 1946 was published. Joint work withKentaro Yano (1912–1993) led to the 1953 bookCurvature and Betti Numbers. It had consequences, for theKodaira vanishing theory,representation theory, andspin manifolds. Bochner also worked onseveral complex variables (theBochner–Martinelli formula and the bookSeveral Complex Variables from 1948 withW. T. Martin).
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