Salomon Bochner (20 August 1899 – 2 May 1982) was an Austrian
mathematician, known for work in
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.
These theories are usually studied ...
,
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...
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
Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...
. There, he was a student of
Erhard Schmidt,
writing a dissertation involving what would later be called the
Bergman kernel In the mathematical study of several complex variables, the Bergman kernel, named after Stefan Bergman, is the reproducing kernel for the Hilbert space (RKHS) of all square integrable holomorphic functions on a domain ''D'' in C''n''.
In deta ...
. 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
The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: Ludwig-Maximilians-Universität München) is a public research university in Munich, Germany. It is Germany's sixth-oldest university in continuous operati ...
from 1924 to 1933. His academic career in Germany ended after the
Nazis came to power
Adolf Hitler's rise to power began in the newly established Weimar Republic in September 1919 when Hitler joined the '' Deutsche Arbeiterpartei'' (DAP; German Workers' Party). He rose to a place of prominence in the early years of the party. Be ...
in 1933, and he left for a position at
Princeton University. He was a visiting scholar at the
Institute for Advanced Study in 1945-48. 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
William Marsh Rice University (Rice University) is a private research university in Houston, Texas. It is on a 300-acre campus near the Houston Museum District and adjacent to the Texas Medical Center. Rice is ranked among the top universitie ...
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
Orthodox Judaism is the collective term for the traditionalist and theologically conservative branches of contemporary Judaism. Theologically, it is chiefly defined by regarding the Torah, both Written and Oral, as revealed by God to Moses on ...
.
Mathematical work
In 1925 he started work in the area of
almost periodic function
In mathematics, an almost periodic function is, loosely speaking, a function of a real number that is periodic to within any desired level of accuracy, given suitably long, well-distributed "almost-periods". The concept was first studied by Haral ...
s, simplifying the approach of
Harald Bohr by use of
compactness and
approximate identity arguments. In 1933 he defined the
Bochner integral In mathematics, the Bochner integral, named for Salomon Bochner, extends the definition of Lebesgue integral to functions that take values in a Banach space, as the limit of integrals of simple functions.
Definition
Let (X, \Sigma, \mu) be a mea ...
, as it is now called, for vector-valued functions.
Bochner's theorem
In mathematics, Bochner's theorem (named for Salomon Bochner) characterizes the Fourier transform of a positive finite Borel measure on the real line. More generally in harmonic analysis, Bochner's theorem asserts that under Fourier transform a ...
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
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
For curves, the canon ...
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 manifold In differential geometry, a spin structure on an orientable Riemannian manifold allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry.
Spin structures have wide applications to mathematical ...
s. Bochner also worked on
several complex variables (the
Bochner–Martinelli formula In mathematics, the Bochner–Martinelli formula is a generalization of the Cauchy integral formula to functions of several complex variables, introduced by and .
History
Bochner–Martinelli kernel
For , in \C^n the Bochner–Martinelli ker ...
and the book ''Several Complex Variables'' from 1948 with
W. T. Martin).
Selected publications
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2016 reprint*
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2013 reprint*
2014 reprint*
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See also
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Bochner almost periodic functions
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Bochner–Kodaira–Nakano identity
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Bochner Laplacian
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Bochner measurable function
References
External links
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*
National Academy of Sciences Biographical Memoir*
{{DEFAULTSORT:Bochner, Salomon
1899 births
1982 deaths
20th-century German mathematicians
20th-century American mathematicians
Jewish scientists
Differential geometers
Complex analysts
Mathematical analysts
Measure theorists
PDE theorists
Princeton University faculty
Rice University faculty
Polish Orthodox Jews
American Orthodox Jews
Jews from Galicia (Eastern Europe)
Scientists from Berlin
Institute for Advanced Study visiting scholars
Jewish emigrants from Nazi Germany to the United States