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8 Gubkina St. Moscow,
119991, Russia
Tel.: +7(495) 984 81 41
Fax: +7(495) 984 81 39
Web site: www.mi-ras.ru
E-mail: steklov@mi-ras.ru

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Department of Function Theory

| Seminars | History of the Department | Research Fields | Awards | Publications |
Kashin Boris Sergeevich

Doctor Phys.-Math. Sci., Professor, Academician of RAS, Head of Department, Chief Scientific Researcher
office: 517; tel.: +7 (495) 984 81 41 * 37 84; e-mail: kashin@mi-ras.ru
Personal page: https://homepage.mi-ras.ru/~kashin
Kashin Boris Sergeevich
Besov Oleg Vladimirovich

Doctor Phys.-Math. Sci., Corresponding Member of RAS, Chief Scientific Researcher
office: 519; tel.: +7 (499) 941 01 89, +7 (495) 984 81 41 * 36 67; e-mail: besov@mi-ras.ru
Personal page: https://homepage.mi-ras.ru/~besov/
Principal fields of research: Functional spaces. Imbeddings. Approximation of classes of functions.
Besov Oleg Vladimirovich
Kosov Egor Dmitrievich

Candidate Phys.-Math. Sci., Senior Scientific Researcher
office: 503; tel.: +7 (495) 984 81 41 * 37 89; e-mail: kosov@mi-ras.ru
Principal fields of research: Measure theory, probability theory, infinite dimensional analysis.
Malykhin Yuri Viatcheslavovich

Candidate Phys.-Math. Sci., Senior Scientific Researcher
office: 502; tel.: +7 (495) 984 81 41 * 37 88, +7 (495) 984 81 41 * 36 64; e-mail: malykhin@mi-ras.ru
Malykhin Yuri Viatcheslavovich
Shaposhnikov Aleksander Valer'evich

Candidate Phys.-Math. Sci., Scientific Researcher
office: 502; e-mail: ashaposhnikov@mi-ras.ru
Tyulenev Alexander Ivanovich

Candidate Phys.-Math. Sci., Senior Scientific Researcher
office: 502; tel.: +7 (495) 984 81 41 * 37 88; 36 64; e-mail: tyulenev@mi-ras.ru

Oskolkov Konstantin Il'ich

Doctor Phys.-Math. Sci., Professor, Out-Of-Staff Member
e-mail: oskolkov@math.sc.edu
Personal page: http://www.math.sc.edu/konstantin-oskolkov
Stepanov Vladimir Dmitrievich

Doctor Phys.-Math. Sci., Professor, Corresponding Member of RAS, Leading Scientific Researcher
office: 518; tel.: +7 (495) 984 81 41 * 3777, +7 (495) 984 81 41 * 3652; e-mail: stepanov@mi-ras.ru
Temlyakov Vladimir Nikolaevich

Doctor Phys.-Math. Sci., Professor, Out-Of-Staff Member
e-mail: temlyak@math.sc.edu
Personal page: http://www.math.sc.edu/people/temlyakov.html

Bochkarev Sergei Viktorovich (24.07.1941 – 08.07.2021)

Doctor Phys.-Math. Sci.

Principal fields of research: Trigonometric and orthogonal series. Functional spaces. Bases and almost everywhere convergence.
Bochkarev Sergei Viktorovich  (24.07.1941 – 08.07.2021)
Kudryavtsev Lev Dmitrievich (25.03.1923 – 17.02.2012)

Doctor Phys.-Math. Sci., Corresponding Member of RAS

Principal fields of research: Locally compact spaces. Function spaces. Embedding theorems. Boundary-value problems. Differential equations. Variational methods. Singular points. Asymptotics of solutions. Extension of solutions. Spaces of functions with given asymptotics. Almost normed spaces.
Nikolskii Sergei Mikhailovich (30.04.1905 – 9.11.2012)

Doctor Phys.-Math. Sci., Academician of RAS

Principal fields of research: Calculus. Polynomial approximations. Variational methods. Boundary-value problems.
Pokhozhaev Stanislav Ivanovich (24.08.1935 – 30.01.2014)

Doctor Phys.-Math. Sci., Professor, Corresponding Member of RAS

Personal page: https://homepage.mi-ras.ru/~pokhozhaev
Principal fields of research: Nonlinear functional analysis. Nonlinear PDE's. Nonlinear variational problems.
Telyakovskii Sergei Aleksandrovich (22.12.1932 – 05.05.2020)

Doctor Phys.-Math. Sci., Professor, Leading Scientific Researcher

Principal fields of research: Approximations of functions. Special trigonometric series. Extreme properties. Functions with bounded variation.Widths.
Telyakovskii Sergei Aleksandrovich  (22.12.1932 – 05.05.2020)
Volkov Evgenii Alekseevich (04.04.1926 – 14.01.2019)

Doctor Phys.-Math. Sci.

Principal fields of research: Differential equations. Difference methods. Exponentially convergent block method for solving boundary problems for the Laplace equation on polygons and the conformal mapping of multiconnected polygons onto canonical domains.
Volkov Evgenii Alekseevich (04.04.1926 – 14.01.2019)
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
Seminar organizer: O. V. Besov
Steklov Mathematical Institute, Room 530 (8 Gubkina)

Seminar on Approximation Theory
Seminar organizer: S. A. Telyakovskii
History of the Department

The Department of Function Theory was organized in1934, on the basis of the Department with the same name at the Institute of Physics and Mathematics of the Academy of Sciences of the USSR, when after a removal from Leningrad to Moscow that institute was divided into two independent institutes, Steklov Mathematical Institute and Physical Institute after P.N.Lebedev. The Department became at once one of leading mathematical centers on function theory in the world and keeps this state up to now. Members of the Department carry out investigations of classical and new problems of mathematical analysis, as well as develop new methods of studying actual problems of function theory. Many received results are on a level with the highest world achievements and often predetermine further development of mathematics in corresponding areas.

At different years, the Department was headed by world-known mathematicians, N.N.Luzin, M.A.Lavrent'ev, S.M.Nikolskii.

N.N.Luzin was the founder of a large mathematical school. His works on the theory of trigonometric series, metric function theory, and the theory of functions of complex variables long ago became classical. They were successfully developed by members of the Department, his students and followers: Academicians B.S.Kashin, P.S.Novikov, P.L.Ul'yanov, Correspondent Members of Academy L.V.Keldysh, D.E.Men'shov, Doctors of Phys.-Math. Sci. S.V.Bochkarev, K.I.Oskolkov, S.A.Telyakovskii, and V.N.Temlyakov. N.N.Luzin was one of the founders of descriptive function theory. Of prime importance are projective sets discovered by N.N.Luzin. He supposedand this hypothesis was confirmed laterthat for these sets one can not solve (inaclassical sense) aseries of problems, including the problem of measurability of projective sets. These works lent impetus to investigations in mathematical logic (P.S.Novikov).

D.E.Men'shov was a member of the Department from its founding. He developed the theory of trigonometric and orthogonal series, as well as the theory of monogenic functions and conformal mappings. In1951, he was awarded the State Prize for his fundamental investigations of the problem of representation of functions by trigonometric series, and in1975 he was awarded the Chebyshev Prize of the USSR Academy of Sciences, for his work on summation of trigonometric series.

M.A.Lavrent'ev developed variational principles of conformal mappings and received a series of fundamental results on boundary properties of analytical functions and on approximations of continuous functions in a complex area by polynomials. He solved a series of crucial problems of theory of quasiconformal mappings. For these results he was awarded by State Prize in1946 and by Lenin Prize in1958. His follower, Correspondent Member of Academy A.V.Bitsadze, applied methods of functions of complex variable to solve a series of important in essence problems of theory of partial differential equations, including equations of mixed type. Correspondent Member of Academy A.F.Leont'ev developed theory of exponent series.

Theory of approximation of functions was one of growing areas in the Department. Researches in this direction were carried out by Academicians S.N.Bernshtein, A.A.Gonchar, M.V.Keldysh, M.A.Lavrent'ev, S.M.Nikol'skii, Correspondent Member of Academy S.N.Mergelyan, and others. In1942, for fundamental results on theory of approximation of functions S.N.Bernshtein was awarded the State Prize.

In 1952, for a circle of works on the best approximation of functions of complex variable S.N.Mergelyan was awarded the State Prize.

Since 1960 until 1988, the Department was headed by Academician S.M.Nikol'skii, and since 1988 until1994, the Department was headed by Correspondent Member of Academy L.D.Kudryavtsev, since1994 until 2020 the Department was headed by Correspondent Member of Academy O.V.Besov. Since 2020 Academician B. S. Kashin is the Head of the Department. At present the staff of the department includes Correspondent Members of Academy S.V.Konyagin, S.I.Pokozhaev, Doctors of Phys.-Math. Sci. S.V.Bochkarev, and Candidate of Phys.-Math. Sci. Yu.V.Malykhin.

More than 45 years ago, S.M.Nikol'skii organized the scientific-research seminar on theory of smooth functions of many variables which is working in the Department. S.M.Nikol'skii is leaderships of this worldly recognized seminar. Atdifferent times V.I.Kondrashov, L.D.Kudryavstev, and S.L.Sobolev were leaderships of the seminar.

Research Fields

In a series of works, S. M. Nikolskii established a link between smoothness of functions, their approximations, and embedding of classes of functions, and for the first time developed a consistent theory of embeddings of functional spaces. These works served as a basis for more in-depth study of theory of differentiable functions of many variables in its applications to variational methods (S.M.Nikol'skii and his followers O. V. Besov, L. D. Kudryavtsev, and P. I. Lizorkin). In 1972, for the Monograph "Approximation of Functions of Many Variables and Embedding Theorems" S. M. Nikolskii received the Chebyshev Prize of the USSR Academy of Sciences. In 1977, for the Monograph "Integral Representations of Functions and Embedding Theorems" O. V. Besov, V. I. Il'in, and S. M. Nikolskii were awarded the State Prize.

The theory of embeddings of functional spaces of differentiable functions was developed in the Department (O. V. Besov, L. D. Kudryavtsev, P. I. Lizorkin, and S. M. Nikolskii). In 1988, for a series of works on boundary problems for differential operators and their applications in mathematical physics, Academician O. A. Oleinik and Correspondent Member of Academy L. D. Kudryavtsev were awarded the State Prize. O. A.Oleinik was awarded the Chebyshev Prize of the USSR Academy of Sciences (1952), the Lomonosov Prize (1964, for a circle of works on mathematical problems in theory of boundary layer), the Petrovskii Prize of the Russian Academy of Sciences (1995, for a cycle of works on asymptotic methods in mathematical physics).

Theory of orthogonal series was actively developed in the Department. In particular,

  • many-sided investigations of series into Haar components and their applications were subjected (P. L. Ul'yanov);
  • important results were received for problems of convergence and summability of Fourier series in classical and general systems (S. V. Bochkarev, B. S. Kashin, K. I. Oskolkov, S. B. Stechkin, S. A. Telyakovskii, and P. L. Ul'yanov);
  • a circle of principal problems of constructing a basis in functional spaces was solved (S. V. Bochkarev);
  • valuable results were received for theoretical problems of theory of best approximations in Banach spaces (S. B. Stechkin), estimates for widths of function classes (B. S. Kashin, S. B. Stechkin, and V. N. Temlyakov), approximation of functions of many variables by harmonic polynomials and bilinear forms (P. I. Lizorkin, S. M. Nikolskii, and V. N. Temlyakov);
  • both probabilistic (S. V. Bochkarev and B. S. Kashin) and geometrical (B. S. Kashin) methods of investigating orthogonal series and approximations of functions were developed;
  • in-depth investigations were carried out for group representation theory, spectral theory of linear operators, and functional analysis (M. A. Naimark);
  • for a circle of works on metric function theory, P. L. Ul'yanov was awarded the State Prize of Russian Federation (1993).

New estimates for mistakes of quadrature and cubature formulae in numerical analysis were obtained (S. M. Nikolskii and S. L. Sobolev); convergence estimates for difference approximate methods of solving boundary problems for the Laplace and Poisson equations were obtained; an exponentially convergent block method was proposed to solve boundary problems for the Laplace equation on polygons and the conformal mappings of multiply connected polygons on canonical regions (E. A. Volkov).

During 1984–1989, Academician S. L. Sobolev had an appointment in the Department. For this time S. L. Sobolev completed a preparation of revised model of his classical Monograph "Some applications of functional analysis in mathematical physics" (3rd ed., Moscow, Nauka, 1988).

In the area of nonlinear analysis, a new constructive method of variational calculus (the so-called method of global stratification) was developed; based on this method, a solvability of a wide class of essentially nonlinear elliptic problems was proved; using the variational Pokhozhaev identities a solvability of elliptic problems in a space with supercritical nonlinearity index was studied;. the new conception of "nonlinear capacity" was attracted to create a new theory of absence of solutions for nonlinear problems of elliptic, parabolic, and hyperbolic types, including multidimensional hyperbolic equations (Correspondent Member of Academy S. I. Pokhozhaev).

Problems of spectral theory of selfadjoint and nonselfadjoint operators are investigating, as well as problems of convergence of spectral expansions and relations of this theory to the problem of complete integrability of nonlinear differential equations (Academician V. A. Il'in).

Asymptotic behaviour of solutions of nonlinear partial differential equations was investigated (Academician O. A. Oleinik).

The theory of averaging for differential equations was developed and its applications in physics, mechanics and engineering sciences are studied (O. A. Oleinik).


The members of the Department were awarded the following State and Academy Prizes:

S. M. Nikolskii
The State Prize (1952)
The Chebyshev Prize of the USSR Academy of Sciences (1972);
The Vinogradov Prize (1985);
The State Prize of Ukraine (1994);
The Kolmogorov Prize (2000);
The Ostrogradskii Prize of National Academy of Sciences of Ukraine (2000);
O. V. Besov, V. P. Il'in, and S. M. Nikolskii
The State Prize (1977);
Ya. S. Bugrov and S. M. Nikol'skii
The State Prize (1987);
Yu. V. Egorov, V. A. Kondrat'ev, L. D. Kudryavtsev, and O. A. Oleinik
The State Prize (1988);
L. D. Kudryavtsev
The Moscow Mathematical Society Prize (1954);
O. V. Besov
The Moscow Mathematical Society Prize (1960);
S. V. Bochkarev
The Salem Prize (1977);
E. A. Volkov
The Prize of Division of Mathematics, USSR Academy of Sciences (1988);
The MAIK/NAUKA Prize for the best publication (1998);
B. S. Kashin
The Moscow Mathematical Society Prize (1988);
S. A. Telyakovskii
The Premium of RFFI for best scientific-popular paper (1998);


International contacts

Members of the Department were invited as speakers at many International Mathematical Congresses:

S. M. Nikol'skii (Amsterdam, 1954)
A. A. Gonchar (Moscow, 1966)
P. L. Ul'yanov (Nice, 1970)
S. V. Bochkarev (Helsinki, 1978)
B. S. Kashin (Warszawa, 1983)

List of publications
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