Israel Gelfand
Israel Moissejewitsch Gelfand (Russian Израиль Моисеевич Гельфанд; * 20 Augustjul / September 2 1913greg in Krasni Okny in the district of Odessa, Russian Empire, now Ukraine, .. † October 5, 2009 in New Brunswick, New Jersey) was a Soviet mathematician.
Life
Gelfand began in 1932 a degree in mathematics from Moscow State University with Andrei Kolmogorov in the field of functional analysis, from which he graduated in 1935 with a dissertation on abstract functions and linear operators. During this time he worked with Abraham Plessner and Lasar Aronowitsch Ljusternik. He habilitated in 1938 ( also at Moscow State University ) for Scientiae Doctor with a thesis on commutative normed algebras. From 1941 to 1990 he held a professorship at the Moscow State University. From 1968 to 1970 Gelfand was president of the Moscow Mathematical Society and was following her an honorary member. In 1990 he moved to the United States and has since worked at Rutgers University in New Jersey, where he was professor of mathematics and biology.
In addition to his research activities Gelfand is also known for its very influential Seminar on Functional Analysis at Moscow State University, which was founded in 1943 and continues at Rutgers University. In the famous seminary of Gelfand met regularly he founded the Moscow school of mathematicians who dealt in particular with representation theory and functional analysis. In addition, he initiated a distance learning program for mathematics, the Gelfand Correspondence Program in Mathematics ( GCPM ), after he had already conducted similar programs in the Soviet Union.
After Gelfand various mathematical concepts are named, among others, the Gelfand transformation, the set of Gelfand - Neumark, the Gelfand - Neumark - Segal construction, the set of Gelfand - Mazur and Gelfandsche Raumtripel. The work of Gelfand played a major role in the history of the Atiyah-Singer index theorem. Since the 1960s, he also dealt with applications of mathematics in biology. With Boris Levitan, he developed the Gelfand - Levitan theory of inverse scattering theory of Sturm- Liouville operators ( 1951).
His son Sergei Gelfand is also a mathematician.
Honors
Gelfand was a member of the Soviet and Russian Academy of Sciences ( corresponding member since 1953, full member since 1984), the American Academy of Arts and Sciences in Boston since 1964, the London Mathematical Society since 1967, the Royal Irish Academy in Dublin since 1970, the National Academy of Sciences of the USA since 1970, the Royal Swedish Academy of Sciences in Stockholm since 1974, the Académie des Sciences de l'Institut of France since 1976, the Royal Society in London since 1977, the Accademia dei Lincei since in 1988 and the Japan Academy of Sciences since 1989, the New York Academy of Sciences since 2000 and of the European Academy of Sciences since 2004.
In 1970 he gave a plenary lecture at the ICM in Nice (The Cohomology of Infinite Dimensional Lie Algebras, Some Questions of Integral Geometry ), as well as in 1962 in Stockholm ( Automorphic functions and the theory of representations ) and in 1954 in Amsterdam ( Some Aspects of Functional Analysis and algebra).
In the Soviet Union Gelfand was awarded the Lenin Prize (1953), the Stalin Prize (1951 and 1953), three times the Order of Lenin (1954, 1956 and 1973 ), twice the Red Banner of Labor ( 1963, 1983) and the Order of Friendship of Peoples (1975).
Gelfand was awarded honorary doctorates from the universities of Oxford ( 1973), Paris VI and VII (1974 ), Harvard (1976 ), Uppsala (1977 ), Lyon ( 1984), Pisa ( 1985), New York ( 1988), Kyoto (1989 ), Pennsylvania (1990), New York (1992) and Rutgers (1993).
Bibliography
Gelfand has published over 800 works and 30 books. The work published mainly in Russian, but have been translated into English for the most part, some books also into German. Some important works are
- Generalized functions: Volume I, Generalized functions, and calculating with them, Berlin, German Academic Publishers 1960 Shilov
- Volume II, Linear topological spaces, spaces of real functions and generalized functions, with Shilov, Berlin, German Academic Publishers 1962
- Volume III, Some questions in the theory of differential equations, Berlin, German Academic Publishers 1964, with Shilov
- Volume IV, Some applications of harmonic analysis: Gelfandsche Raumtripel, Berlin, German Academic Publishers 1964 Naum Wilenkin
- Volume V Integral geometry and representation theory, Moscow, 1962, MI Graev and Naum Wilenkin ( in Russian) (English translation: "Integral geometry and representation theory", Academic Press 1966)
- Volume VI Representation Theory and automorphic functions with Ilya Pjatetskij - Shapiro, MI Graev, Academic Press 1990
In addition, Gelfand published a number of other mathematical textbooks and monographs such as:
- With A. Shen algebra, Birkhäuser 1993
- With Mikhail Kapranow, Andrei Zelevinsky Discriminants, resultants, and multidimensional determinants, Birkhäuser 2008
- Functions and their graphical representation, Teubner 1971, Harri German 1972
- Lectures on Linear Algebra, Dover 1989
- With E. G. Glagoleva, Alexander Kirillov Method of coordinates, Birkhauser 1990
- With Gindikin, M. Graev Selected topics in integral geometry, American Mathematical Society 2003
- With RA Minlos, Z. Shapiro Representations of the rotation and Lorentz groups and Their application, Pergamon Press 1963
- Unitary representations with Mark Naimark of classical groups, Berlin, Akademie Verlag 1957
- With Mark Saul Trigonometry, Birkhauser 2001
Important works include Gelfand
- On the embedding of a normed ring into a ring of operators in a Hilbert space ( with Neumark ), Mat Sbornik 12 (54, 1943), 197-217
- Irreducible unitary representations of locally compact groups ( with Raikov ), Mat Sbornik 13 (55, 1943), 301-316