Salomon Bochner Explained

Salomon Bochner
Birth Date:20 August 1899
Birth Place:Podgórze, Austria-Hungary
Death Place:Houston, Texas
Fields:Mathematics
Alma Mater: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[1]
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[2] [3]

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 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 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 at Princeton University. He was a visiting scholar at the Institute for Advanced Study in 1945 to 1948.[4] 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 Department at Rice in 1969 and held this position until 1976. He died in Houston, Texas. He was an Orthodox Jew.[5]

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 from 1946 was published. 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 several complex variables (the Bochner–Martinelli formula and the book Several Complex Variables from 1948 with W. T. Martin).

Selected publications

See also

External links

Notes and References

  1. Web site: Bernard Russell Gelbaum . Mathematics Genealogy Project . 28 March 2021.
  2. Web site: [the st-and.ac.uk "Biography" entry for] Salomon Bochner ].
  3. Web site: [the st-and.ac.uk "Society Prizes" entry for] The Leroy P Steele Prize of the AMS ]. 8 January 2015 . 9 June 2015 . https://web.archive.org/web/20150609043245/http://www-groups.dcs.st-and.ac.uk/~history/Societies/AMSSteelePrize.html . dead .
  4. http://www.ias.edu/people/cos/ Institute for Advanced Study: A Community of Scholars
  5. Web site: Bochner biography . 25 February 2008 . 7 November 2019 . https://web.archive.org/web/20191107005709/http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Bochner.html . dead .
  6. 10.1090/S0002-9904-1933-05565-9. Book Review: Vorlesungen über Fouriersche Integrale. 1933. Franklin. Philip. Philip Franklin. Bulletin of the American Mathematical Society. 39. 3. 184–185. free.
  7. 10.2307/3611424. 3611424. Cooper. J. L. B.. Reviewed work: Several Complex Variables Salomon Bochner, William Ted Martin. The Mathematical Gazette. 1949. 33. 305. 218–220.
  8. 10.1090/S0002-9904-1950-09436-1. Book Review: Fourier transforms. 1950. Segal. I. E.. Irving Segal. Bulletin of the American Mathematical Society. 56. 6. 526–529. free.
  9. 10.1090/S0002-9904-1954-09834-8. Book Review: Curvature and Betti numbers. 1954. Boothby. William M.. Bulletin of the American Mathematical Society. 60. 4. 404–406.
  10. 10.1086/350200. Cannon, Walter F.. Review of The Role of Mathematics in the Rise of Science by Salomon Bochner. Isis. 1967. 58. 119–120.