Andrey Nikolayevich Tychonoff

Infobox_Scientist
name = Andrey Tychonoff


image_width = 180px
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birth_date = birth date|1906|10|30|df=y
birth_place = Gzhatsk, Russian Empire
death_date = death date and age|1993|11|8|1906|10|30
death_place = Moscow, Russia
residence =
citizenship = flag|Russian Empire
flag|USSR
flag|Russia
nationality = Russia
ethnicity = Russian
field = mathematics
work_institution = 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.
author_abbreviation_bot =
author_abbreviation_zoo =
prizes =
religion =
footnotes =

Andrey Nikolayevich Tychonoff ( _ru. Андрей Николаевич Тихонов) (October 30, 1906, Gzhatsk – November 8, 1993, Moscow) was a Russian mathematician know 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.

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.

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 [cite journal|author=A. Tychonoff|title=Théorèmes d'unicité pour l'équation de la chaleur|journal=Mathematical Sbornik|volume=42:2|pages=199–216|year=1935|url= http://mi.mathnet.ru/eng/msb6410] 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 [cite journal|author=A. N. Tikhonov|title=Systems of Differential Equations Containing Small Parameters in the Derivatives|journal=Mathematical Sbornik|volume=31(73):3|pages=575–586|year=1952|url= http://mi.mathnet.ru/eng/msb5548] .

Awards

Tychonoff received numerous honors and awards for his work, including the Lenin Prize (1966) and the Hero of Socialist Labor (1954, 1986).

Publications

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.

Papers

ee also

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*MathGenealogy|id=58042