Prof Sergei Lvovich Sobolev (russian: Серге́й Льво́вич Со́болев) H FRSE (6 October 1908 – 3 January 1989) was a

Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nation ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

working in

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

and partial differential equations. Sobolev introduced notions that are now fundamental for several areas of mathematics.

Sobolev space In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense ...

s can be defined by some growth conditions on the Fourier transform. They and their embedding theorems are an important subject in

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...

Generalized function In mathematics, generalized functions are objects extending the notion of functions. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful in making discontinuous functions ...

s (later known as distributions) were first introduced by Sobolev in 1935 for

weak solution In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precis ...

s, and further developed by

Laurent Schwartz Laurent-Moïse Schwartz (; 5 March 1915 – 4 July 2002) was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields Medal in ...

. Sobolev abstracted the classical notion of differentiation, so expanding the range of application of the technique of Newton and Leibniz. The theory of distributions is considered now as the calculus of the modern epoch.

Life

He was born in

St. Petersburg Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...

as the son of Lev Alexandrovich Sobolev, a lawyer, and his wife, Natalya Georgievna. His city was renamed Petrograd in his youth and then Leningrad in 1924. Sobolev studied Mathematics at

Leningrad University Saint Petersburg State University (SPBU; russian: Санкт-Петербургский государственный университет) is a public research university in Saint Petersburg, Russia. Founded in 1724 by a decree of Peter the G ...

and graduated in 1929, having studied under Professor Nikolai Günther. After graduation, he worked with Vladimir Smirnov, whom he considered as his second teacher. He worked in Leningrad from 1932, and at the

Steklov Mathematical Institute Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part o ...

in Moscow from 1934. He headed the institute in evacuation to

Kazan Kazan ( ; rus, Казань, p=kɐˈzanʲ; tt-Cyrl, Казан, ''Qazan'', IPA: ɑzan is the capital and largest city of the Republic of Tatarstan in Russia. The city lies at the confluence of the Volga and the Kazanka rivers, covering an ...

during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...

. He was a

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

Professor of Mathematics from 1935 to 1957 and also a deputy director of the Institute for Atomic Energy from 1943 to 1957 where he participated in the

A-bomb A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission bomb) or a combination of fission and fusion reactions ( thermonuclear bomb), producing a nuclear explosion. Both bomb ...

project of the USSR. In 1958, he led with

Nikolay Brusentsov Nikolay Petrovich Brusentsov (russian: Никола́й Петро́вич Брусенцо́в; 7 February 1925 in Kamenskoe, Ukrainian SSR – 4 December 2014) was a computer scientist, most famous for having built a ( balanced) ternary compute ...

the development of the

ternary computer A ternary computer, also called trinary computer, is one that uses ternary logic (i.e., base 3) instead of the more common binary system (i.e., base 2) in its calculations. This means it uses trits (instead of bits, as most computers do). Ty ...

Setun. In 1956, Sobolev joined a number of scientists in proposing a large-scale scientific and educational initiative for the Eastern parts of the

Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

, which resulted in the creation of the Siberian Division of the

Academy of Sciences An academy of sciences is a type of learned society or academy (as special scientific institution) dedicated to sciences that may or may not be state funded. Some state funded academies are tuned into national or royal (in case of the Unit ...

. He was the founder and first director of the Institute of Mathematics at

Akademgorodok Akademgorodok ( rus, Академгородок, p=ɐkəˌdʲemɡərɐˈdok, "Academic Town") is a part of the Sovetsky City District, Novosibirsk, Sovetsky District of the city of Novosibirsk, Russia, located south of the city center and abou ...

near Novosibirsk, which was later to bear his name, and played an important role in the establishment and development of

Novosibirsk State University Novosibirsk State University is a public research university located in Novosibirsk, Russia. The university was founded in 1958, on the principles of integration of education and science, early involvement of students with research activities an ...

. In 1962, he called for a reform of the Soviet education system. He died in

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 millio ...

Family

In 1930 he married Ariadna Dmitrievna.

Publications

In 1955 he co-wrote ''

The Main Features of Cybernetics "The Main Features of Cybernetics" (russian: Основные черты кибернетики) was a key text which led to the emergence of cybernetics in the Soviet Union, published in July–August 1955 volume of the state philosophical organ, ' ...

'' with

Alexey Lyapunov Alexey Andreevich Lyapunov (russian: Алексе́й Андре́евич Ляпуно́в; 25 September 1911 – 23 June 1973) was a Soviet mathematician and an early pioneer of computer science. One of the founders of Soviet cybernetics ...

and

Anatoly Kitov Anatoly Ivanovich Kitov (9 August 1920, Samara - 14 October 2005) was a pioneer of cybernetics in the Soviet Union Cybernetics in the Soviet Union had its own particular characteristics, as the study of cybernetics came into contact with th ...

which was published in ''

Voprosy filosofii ''Voprosy Filosofii'' (russian: Вопросы философии, ''Problems of Philosophy'') is a Soviet and Russian scientific and theoretical philosophical peer-reviewed academic journal. It was established in July 1947 under the guidance of t ...

''.

Notes

References

* (in French). In this paper Sergei Sobolev introduces

generalized function In mathematics, generalized functions are objects extending the notion of functions. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful in making discontinuous functions ...

s, applying them to the problem of solving

linear Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear ...

hyperbolic partial differential equation In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first n-1 derivatives. More precisely, the Cauchy problem can be ...

s. * (in

Russian Russian(s) refers to anything related to Russia, including: *Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *Rossiyane (), Russian language term for all citizens and peo ...

, with French

summary may refer to: * Abstract (summary), shortening a passage or a write-up without changing its meaning but by using different words and sentences * Epitome, a summary or miniature form * Abridgement, the act of reducing a written work into a sho ...

). In this paper Sergei Sobolev proved his embedding theorem, introducing and using

integral operator An integral operator is an operator that involves integration. Special instances are: * The operator of integration itself, denoted by the integral symbol * Integral linear operators, which are linear operators induced by bilinear forms invol ...

s very similar to

mollifier In mathematics, mollifiers (also known as ''approximations to the identity'') are smooth functions with special properties, used for example in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) f ...

s, without naming them.

Bibliography

*
''Sergei Lvovich Sobolev (1908-1989). Bio-Bibliography''
( S.S. Kutateladze, editor) Novosibisrk, Sobolev Institute (2008),
''Sergei Lvovich Sobolev.''
in: Russian Mathematicians in the 20th Century (

Yakov Sinai Yakov Grigorevich Sinai (russian: link=no, Я́ков Григо́рьевич Сина́й; born September 21, 1935) is a Russian-American mathematician known for his work on dynamical systems. He contributed to the modern metric theory of dy ...

, editor), pp. 381–382.

World Scientific Publishing World Scientific Publishing is an academic publisher of scientific, technical, and medical books and journals headquartered in Singapore. The company was founded in 1981. It publishes about 600 books annually, along with 135 journals in various f ...

, 2003. *Jean Leray. ''La vie et l'œuvre de Serge Sobolev''. he life and works of Sergeĭ Sobolev Comptes Rendus de l'Académie des Sciences. Série Générale. La Vie des Sciences, vol. 7 (1990), no. 6, pp. 467–471. *G. V. Demidenko
''A GREAT MATHEMATICIAN OF 20th CENTURY. On the occasion of the centenary from the birthdate of Sergei Lvovich Sobolev''.
Science in Siberia, no. 39 (2674), 2 October 2008 *M. M. Lavrent'ev, Yu. G. Reshetnyak, A. A. Borovkov, S. K. Godunov, T. I. Zelenyak and S. S. Kutateladze. ''Remembrances of Sergei L'vovich Sobolev.'' Siberian Mathematical Journal, vol. 30 (1989), no. 3, pp. 502–504

External links

* *

* Kutateladze S.S.br>Sobolev and Schwartz: Two Fates and Two Fames
* Kutateladze S.S.br>Sobolev of the Euler school
* :ru:Соболев, Сергей Львович
Sobolev's Biography in Russian
{{DEFAULTSORT:Sobolev, Sergei Lvovich 1908 births 1989 deaths Mathematicians from Saint Petersburg Soviet mathematicians Russian inventors Full Members of the USSR Academy of Sciences Saint Petersburg State University alumni Moscow State University faculty Moscow Institute of Physics and Technology faculty Members of the French Academy of Sciences Stalin Prize winners Heroes of Socialist Labour Members of the German Academy of Sciences at Berlin