Salomon Bochner

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 American mathematician of Austrian-Hungarian origin, known for wide-ranging 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. He studied at the University of Warsaw. 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 died in Houston, Texas. He was an Orthodox 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 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 most influential. Joint work with Kentaro Yano (1912-1993) led to the 1953 book "Curvature and Betti Numbers". It had broad 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).

See also

* Bochner identity
* Bochner space

econdary literature

* Cooke, Roger, 2005, "Lectures on Fourier integrals" in Grattan-Guinness, I., ed., "Landmark Writings in Western Mathematics". Elsevier: 945-59.

References

External links

*
*


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Salomon Bochner — (* 20. August 1899 in Podgórze bei Krakau, heute Polen; † 2. Mai 1982 in Houston, Texas) war ein US amerikanischer Mathematiker, der auf dem Gebiet der Analysis (z. B. Harmonische Analyse, fastperiodische Funktionen, mehrere komplexe Variable,… …   Deutsch Wikipedia

  • Salomon Bochner — Pour les articles homonymes, voir Bochner. Salomon Bochner (20 août 1899 2 mai 1982) est un mathématicien américain d’origine austro hongroise, connu pour ses travaux en analyse, en théorie des probabilités et en géométrie différentielle.… …   Wikipédia en Français

  • Bochner — is the surname of: * Hart Bochner * Lloyd Bochner * Mel Bochner * Salomon Bochner (1899 1982), American mathematician See also * Büchner …   Wikipedia

  • Bochner-Integral — Das Bochner Integral, benannt nach Salomon Bochner, ist eine Verallgemeinerung des Lebesgue Integrals auf Banachraum wertige Funktionen. Inhaltsverzeichnis 1 Definition 2 Messbarkeitssatz von Pettis 3 Bochner Integrierbarkeit …   Deutsch Wikipedia

  • Bochner integral — In mathematics, the Bochner integral extends the definition of Lebesgue integral to functions which take values in a Banach space.The theory of vector valued functions is a chapter of mathematical analysis, concerned with the generalisation to… …   Wikipedia

  • Bochner space — In mathematics, Bochner spaces are a generalization of the concept of Lp spaces to more general domains and ranges than the initial definition, specifically by replacing the Lebesgue integral with the Bochner integral. They are often used in the… …   Wikipedia

  • Bochner — Den Namen Bochner tragen folgende Personen: Hart Bochner, kanadischer Schauspieler Lloyd Bochner, dessen Vater, ebenfalls kanadischer Schauspieler Mel Bochner, US amerikanischer Konzeptkünstler Salomon Bochner, US amerikanischer Mathematiker,… …   Deutsch Wikipedia

  • Bochner — Cette page d’homonymie répertorie les différents sujets et articles partageant un même nom. Bochner: Hart Bochner, un acteur, réalisateur, scénariste et producteur canadien,(1956 ). Lloyd Bochner, un acteur canadien, (1924 2005). Salomon Bochner …   Wikipédia en Français

  • Bochner identity — In mathematics mdash; specifically, differential geometry mdash; the Bochner identity is an identity concerning harmonic maps between Riemannian manifolds. The identity is named after the American mathematician Salomon Bochner.tatement of the… …   Wikipedia

  • Bochner, Salomon — ▪ American mathematician born , August 20, 1899, Podgorze (near Kraków), Austria Hungary [now in Poland] died May 2, 1982, Houston, Texas, U.S.       Galician born American mathematician who made profound contributions to harmonic analysis,… …   Universalium

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”