| Salomon Bochner | |
| Fields | 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. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval A doctorate is an Academic degree that indicates the highest level of academic achievement Erhard Schmidt ( January 13, 1876 – December 6, 1959) was a German Mathematician born in Dorpat (now Richard Allen Askey (born June 4 1933) is an American Mathematician, known for his expertise in the area of Special functions Jeff Cheeger (b December 1, 1943, Brooklyn, New York City) is a Mathematician. Hillel (Harry Furstenberg (הלל (הארי פורסטנברג is an Israeli Mathematician, a member of the Israel Academy of Sciences and Humanities and U Israel Halperin ( January 5, 1911 &ndash March 8, 2007) was a Canadian Mathematician and social activist. In Mathematics, the Bochner integral extends the definition of Lebesgue integral to functions which take values in a Banach space. In Mathematics, Bochner's theorem characterizes the Fourier transform of a positive finite Borel measure on the real line Events 636 - Battle of Yarmouk: Arab forces led by Khalid ibn al-Walid take control of Syria and Palestine Year 1899 ( MDCCCXCIX) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar (or a Common Events 1194 - King Richard I of England gives Portsmouth its first Royal Charter. Year 1982 ( MCMLXXXII) was a Common year starting on Friday (link displays the 1982 Gregorian calendar) The United States of America —commonly referred to as the A mathematician is a person whose primary area of study and research is the field of Mathematics. Analysis has its beginnings in the rigorous formulation of Calculus. Probability theory is the branch of Mathematics concerned with analysis of random phenomena Differential geometry is a mathematical discipline that uses the methods of differential and integral Calculus to study problems in Geometry
Contents |
Life
He was born into a Jewish Family in Podgórze (near Kraków), then Austria-Hungary, now Poland. Kraków, in English also spelled Krakow or Cracow (ˈkrækaʊ M-W: krăk'ou krāk'ō is one of the largest and oldest cities in Poland Poland (Polska officially the Republic of Poland He studied at the University of Warsaw. University of Warsaw (Uniwersytet Warszawski is the largest University in Poland, ranked by the Times Higher Education Supplement as the second best Polish Fearful of a Russian invasion in Galicia at the beginning of World War I in 1914, his family moved to Germany, seeking greater security. Galicia (Галичина ( Halychyna) Galicja is a historical region in East Central Europe, currently divided between Poland and Ukraine, World War I (abbreviated WWI; also known as the First World War, the Great War, and the War to End All Year 1914 ( MCMXIV) was a Common year starting on Thursday (link will display the full calendar of the Gregorian calendar (or a Common year Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. 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. Erhard Schmidt ( January 13, 1876 – December 6, 1959) was a German Mathematician born in Dorpat (now In Functional analysis (a branch of Mathematics) a reproducing kernel Hilbert space is a Hilbert space of functions in which pointwise evaluation Shortly after this, he left the academy to help his family during the escalating inflation. Certain figures in this article use Scientific notation for readability After returning to mathematical research, he lectured at the University of Munich from 1924 to 1933. The Ludwig Maximilian University of Munich (Ludwig-Maximilians-Universität München also known as LMU, is a University in Munich and with more Year 1924 ( MCMXXIV) was a Leap year starting on Tuesday (link will display the full calendar of the Gregorian calendar. Year 1933 ( MCMXXXIII) was a Common year starting on Sunday (link will display full calendar of the Gregorian calendar. His academic career in Germany ended after the Nazis came to power in 1933, and he left for a position at Princeton University. Year 1933 ( MCMXXXIII) was a Common year starting on Sunday (link will display full calendar of the Gregorian calendar. Princeton University is a private Coeducational research university located in Princeton, New Jersey. He died in Houston, Texas. He was an Orthodox Jew. [1]
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. Year 1925 ( MCMXXV) was a Common year starting on Thursday (link will display the full calendar of the Gregorian calendar. In Mathematics, almost periodic functions are functions of a real number that are periodic up to a small error first studied by Harald Bohr. Harald August Bohr ( 22 April 1887 &ndash 22 January 1951) was a Danish Mathematician and football player In Functional analysis, a right approximate identity in a Banach algebra, A, is a net (or a Sequence) \{\e_\lambda In 1933 he defined the Bochner integral, as it is now called, for vector-valued functions. Year 1933 ( MCMXXXIII) was a Common year starting on Sunday (link will display full calendar of the Gregorian calendar. In Mathematics, the Bochner integral extends the definition of Lebesgue integral to functions which take values in a Banach space. Bochner's theorem on Fourier transforms appeared in a 1932 book. In Mathematics, Bochner's theorem characterizes the Fourier transform of a positive finite Borel measure on the real line This article specifically discusses Fourier transformation of functions on the Real line; for other kinds of Fourier transformation see Fourier analysis and Year 1932 ( MCMXXXII) was a Leap year starting on Friday of the Gregorian calendar. His techniques came into their own as Pontryagin duality and then the representation theory of locally compact groups developed in the following years. In Mathematics, in particular in Harmonic analysis and the theory of Topological groups Pontryagin duality explains the general properties of the Fourier In Mathematics, a locally compact group is a Topological group G which is locally compact as a Topological space.
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. In Mathematics, Bochner's formula is a statement relating Harmonic functions on a Riemannian manifold (M g to the Ricci curvature In Mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry Joint work with Kentaro Yano (1912-1993) led to the 1953 book Curvature and Betti Numbers. Year 1953 ( MCMLIII) was a Common year starting on Thursday (link will display full calendar of the Gregorian calendar. It had broad consequences, for the Kodaira vanishing theory, representation theory, and spin manifolds. In Mathematics, the Kodaira vanishing theorem is a basic result of Complex manifold theory and complex Algebraic geometry, describing general conditions In the mathematical field of Representation theory, group representations describe abstract groups in terms of Linear transformations of In Geometry, a spin structure is an additional piece of data which can sometimes be specified on a Vector bundle over a Differentiable manifold. Bochner also worked on several complex variables (the Bochner-Martinelli formula and the book Several Complex Variables from 1948 with W. The theory of functions of several complex variables is the branch of Mathematics dealing with functions f ( z1 z2 Year 1948 ( MCMXLVIII) was a Leap year starting on Thursday (link will display the 1948 calendar of the Gregorian calendar. T. Martin).
See also
Secondary literature
- Cooke, Roger, 2005, "Lectures on Fourier integrals" in Grattan-Guinness, I., ed. In Mathematics &mdash specifically Differential geometry &mdash the Bochner identity is an identity concerning Harmonic maps between Riemannian In Mathematics, Bochner spaces are a generalization of the concept of ''Lp'' spaces to more general domains and ranges than the initial definition specifically This article specifically discusses Fourier transformation of functions on the Real line; for other kinds of Fourier transformation see Fourier analysis and Ivor Grattan-Guinness (Born 23 June 1941 Bakewell, England is a Historian of mathematics and Logic. , Landmark Writings in Western Mathematics. Elsevier: 945-59.
References
External links
- O'Connor, John J. & Robertson, Edmund F. , “Salomon Bochner”, MacTutor History of Mathematics archive
- Salomon Bochner at the Mathematics Genealogy Project
Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic