Andrey Nikolayevich Tychonoff
From Wikipedia, the free encyclopedia
| Andrey Tychonoff | |
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| Born | 30 October 1906 Gzhatsk, Russian Empire |
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| Died | November 8, 1993 (aged 87) Moscow, Russia |
| Citizenship |  Russian Empire USSR Russia |
| Nationality | Russia |
| Ethnicity | Russian |
| Fields | mathematics |
| Institutions | Moscow State University |
| Alma mater | Moscow State University |
| Doctoral advisor | Pavel Alexandrov |
| Doctoral students | Alexander Samarsky |
| Known for | important contributions to topology, functional analysis, mathematical physics, ill-posed problems; Tychonoff spaces, Tychonoff's theorem, Tikhonov regularization. |
Andrey Nikolayevich Tychonoff (Russian: Андрей Николаевич Тихонов) (October 30, 1906, Gzhatsk – November 8, 1993, Moscow) was a Russian mathematician known for important contributions to topology, functional analysis, mathematical physics, and ill-posed problems. Tychonoff originally published in German, whence the transliteration. The English style "Tikhonov" is also commonly seen.
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[edit] Biography
Born near Smolensk, he studied at the Moscow State University where he received Ph.D. in 1927 under direction of Pavel Sergeevich Alexandrov. In 1933 he was appointed as a professor at Moscow State University. He became a corresponding member of the USSR Academy of Sciences on 29 January 1939 and a full member of the USSR Academy of Sciences on 1 July 1966.
[edit] Research work
Tychonoff worked in a number of different fields in mathematics. He made important contributions to topology, functional analysis, mathematical physics, and certain classes of ill-posed problems. Tikhonov regularization, one of the most widely used methods to solve inverse problems, is named in his honor. He is best known for his work on topology, including the metrization theorem he proved in 1926, and the Tychonoff's theorem, which states that every product of arbitrarily many compact topological spaces is again compact. In his honor, completely regular topological spaces are also named Tychonoff spaces.
In mathematical physics, he proved the fundamental uniqueness theorems for the heat equation[1] and studied Volterra integral equations.
In asymptotical analysis, he founded the theory of asymptotic analysis for differential equations with small parameter in the leading derivative.[2]
[edit] Organizer work
Tychonoff played the leading role in founding Faculty of Computational Mathematics and Cybernetics of Moscow State University and served as its first dean during the period of 1970-1990.
[edit] Awards
Tychonoff received numerous honors and awards for his work, including the Lenin Prize (1966) and the Hero of Socialist Labor (1954, 1986).
[edit] Publications
[edit] Books
- A.N. Tikhonov, V.Y. Arsenin, Solutions of Ill-Posed Problems, Winston, New York, 1977. ISBN 0470991240.
- A.N. Tikhonov, A.V. Goncharsky, Ill-posed Problems in the Natural Sciences, Oxford University Press, Oxford, 1987. ISBN 0828537399.
- A.N. Tikhonov, A.A. Samarskii, Equations of Mathematical Physics, Dover Publications, 1990. ISBN 0486664228.
- A.N. Tikhonov, A.V. Goncharsky, V.V. Stepanov, A.G. Yagoda, Numerical Methods for the Solution of Ill-Posed Problems, Kluwer, Dordrecht, 1995. ISBN 079233583X.
[edit] Papers
- ^ A. Tychonoff (1935). "Théorèmes d'unicité pour l'équation de la chaleur". Mathematical Sbornik 42:2: 199–216. http://mi.mathnet.ru/eng/msb6410.
- ^ A. N. Tikhonov (1952). "Systems of Differential Equations Containing Small Parameters in the Derivatives". Mathematical Sbornik 31(73):3: 575–586. http://mi.mathnet.ru/eng/msb5548.
