


Department of Function Theory
 Seminars 
History of the Department 
Research Fields 
Awards 
Publications 


Staff

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; email: kashin@miras.ru Personal page: https://homepage.miras.ru/~kashin


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; email: besov@miras.ru Personal page: https://homepage.miras.ru/~besov/
Principal fields of research:
Functional spaces. Imbeddings. Approximation of classes of functions.


Kosov Egor Dmitrievich Candidate Phys.Math. Sci., Senior Scientific Researcher
office: 503; tel.: +7 (495) 984 81 41 * 37 89; email: kosov@miras.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; email: malykhin@miras.ru


Shaposhnikov Aleksander Valer'evich Candidate Phys.Math. Sci., Scientific Researcher
office: 502; email: ashaposhnikov@miras.ru


Tyulenev Alexander Ivanovich Candidate Phys.Math. Sci., Senior Scientific Researcher
office: 502; tel.: +7 (495) 984 81 41 * 37 88; 36 64; email: tyulenev@miras.ru



Oskolkov Konstantin Il'ich Doctor Phys.Math. Sci., Professor, OutOfStaff Member
email: oskolkov@math.sc.edu Personal page: http://www.math.sc.edu/konstantinoskolkov


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; email: stepanov@miras.ru


Temlyakov Vladimir Nikolaevich Doctor Phys.Math. Sci., Professor, OutOfStaff Member
email: 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.


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. Boundaryvalue 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. Boundaryvalue problems.


Pokhozhaev Stanislav Ivanovich (24.08.1935 – 30.01.2014) Doctor Phys.Math. Sci., Professor, Corresponding Member of RAS
Personal page: https://homepage.miras.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.


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.



Top 
Seminars

Top 
History of the Department
The Department of Function Theory was organized in 1934, 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 worldknown 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 supposed—and this hypothesis was confirmed later—that for these sets one can not solve (in a classical sense) a series 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. In 1951, he was awarded the State Prize for his fundamental investigations of the problem of representation of functions by trigonometric series, and in 1975 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 in 1946 and by Lenin Prize in 1958. 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. In 1942, 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 until 1994, the Department was headed by Correspondent Member of Academy L. D. Kudryavtsev, since 1994 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 scientificresearch 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. At different times V. I. Kondrashov, L. D. Kudryavstev, and S. L. Sobolev were leaderships of the seminar. 
Top 
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 indepth 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,
 manysided 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;
 indepth 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 socalled 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).

Top 
Awards
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 scientificpopular paper (1998);

Top 
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

