Prof Sergei Lvovich Sobolev,

FRSE Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and Literature, letters, judged to be "eminently distinguished in their subject". ...

(; 6 October 1908 – 3 January 1989) was a

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

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, mathematical structure, structure, space, Mathematica ...

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 ( ...

and

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s. 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 In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...

. 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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...

Generalized function In mathematics, generalized functions are objects extending the notion of functions on real or complex numbers. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful for tr ...

s (later known as

distribution Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a varia ...

s) 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 prec ...

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 Distribution (mathematics), distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awar ...

. Sobolev abstracted the classical notion of differentiation, so expanding the range of application of the technique of Newton and Leibniz. The theory of

s is considered now as the calculus of the modern epoch.

Life

He was born in

St. Petersburg Saint Petersburg, formerly known as Petrograd and later Leningrad, is the second-largest city in Russia after Moscow. It is situated on the River Neva, at the head of the Gulf of Finland on the Baltic Sea. The city had a population of 5,601, ...

as the son of Lev Aleksandrovich 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 (SPBGU; ) is a public university, public research university in Saint Petersburg, Russia, and one of the oldest and most prestigious universities in Russia. Founded in 1724 by a decree of Peter the Great, the uni ...

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

Kazan Kazan; , IPA: Help:IPA/Tatar, ɑzanis the largest city and capital city, capital of Tatarstan, Russia. The city lies at the confluence of the Volga and the Kazanka (river), Kazanka Rivers, covering an area of , with a population of over 1. ...

during

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

. He was a

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

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 project of the USSR. In 1958, he led with

Nikolay Brusentsov Nikolay Petrovich Brusentsov (; 7 February 1925 in Kamenskoe, Ukrainian SSR – 4 December 2014) was a computer scientist, most famous for having built a ( balanced) ternary computer, Setun, together with Sergei Sobolev in 1958. In 1970 he desig ...

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. Ternary computers use trits, instead of binary bits. Types of states ...

Setun Setun () was a computer developed in 1958 at Moscow State University. It was built under the leadership of Sergei Sobolev and Nikolay Brusentsov. It was the first modern ternary computer, using the balanced ternary numeral system and three-val ...

. 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 Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

, which resulted in the creation of the Siberian Division of the Academy of Sciences. 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 Novosibirsk is the largest city and administrative centre of Novosibirsk Oblast and the Siberian Federal District in Russia. As of the 2021 Russian census, 2021 census, it had a population of 1,633,595, making it the most populous city in Siber ...

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

Novosibirsk State University Novosibirsk State University (NSU) 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 act ...

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

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

Family

In 1930 he married Ariadna Dmitrievna.

Publications

In 1955 he co-wrote '' The Main Features of Cybernetics'' with

Alexey Lyapunov Alexey Andreyevich Lyapunov (; 8 October 1911 – 23 June 1973) was a Soviet mathematician and an early pioneer of computer science. One of the founders of Soviet cybernetics, Lyapunov was member of the Academy of Sciences of the Soviet Union ...

and

Anatoly Kitov Anatoly Ivanovich Kitov (9 August 1920 – 14 October 2005) was a pioneer of cybernetics in the Soviet Union. Early life and education Anatoly Kitov was born in Samara in 1920. The Kitov family moved to Tashkent in 1921, as Anatoly's father ...

, which was published in '' Problems of Philosophy''.

Notes

References

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

generalized function In mathematics, generalized functions are objects extending the notion of functions on real or complex numbers. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful for tr ...

s, applying them to the problem of solving

linear In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a '' polynomial''. An example of a linear function is the function defined by f(x) ...

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 ...

s. * (in

Russian Russian(s) may refer to: *Russians (), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *A citizen of Russia *Russian language, the most widely spoken of the Slavic languages *''The Russians'', a b ...

, 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 shor ...

). 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 involvi ...

s very similar to

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

s, without naming them.

Bibliography

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

Yakov Sinai Yakov Grigorevich Sinai (; born September 21, 1935) is a Russian–American mathematician known for his work on dynamical systems. He contributed to the modern metric theory of dynamical systems and connected the world of deterministic (dynam ...

, 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, with more than 170 journals in var ...

, 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 Lvovich Sobolev.'' Siberian Mathematical Journal, vol. 30 (1989), no. 3, pp. 502–504