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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 |
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; 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
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., 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)
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Seminars
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
Steklov Mathematical Institute, Room 502 (8 Gubkina)
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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.

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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).

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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 scientific-popular paper (1998);

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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)

Recent publications

Steklov Mathematical Institute staff Steklov Mathematical Institute staff and out-of-staff employees
| by years | scientific publications | by types |



   2022
1. A. I. Tyulenev, “Restrictions of Sobolev $W^{1}_{p}(\mathbb{R}^{2})$-spaces to planar rectifiable curves”, Ann. Acad. Sci. Fenn. Math., 47 (2022) (to appear) , arXiv: 2010.05286 (25pp)

   2021
2. Funktsionalnye prostranstva, teoriya priblizhenii i smezhnye voprosy analiza, Sbornik statei. K 115-letiyu so dnya rozhdeniya akademika Sergeya Mikhailovicha Nikolskogo, Trudy MIAN, 312, ed. O. V. Besov, A. I. Tyulenev, MIAN, M., 2021 , 338 pp.  mathnet
3. O. V. Besov, “Interpolation of Spaces of Functions of Positive Smoothness on a Domain”, Proc. Steklov Inst. Math., 312 (2021), 91–103  mathnet  crossref  crossref  isi  elib  scopus
4. S. V. Bochkarev, “Inequalities for Orthogonal Series and a Strengthening of the Carleman–Olevskii Theorem for Complete Orthonormal Systems”, Proc. Steklov Inst. Math., 312 (2021), 104–123  mathnet  crossref  crossref  isi  elib  scopus
5. P. A. Borodin, M. I. Dyachenko, B. S. Kashin, T. P. Lukashenko, I. I. Mel'nikov, V. A. Sadovnichii, B. V. Simonov, V. A. Skvortsov, A. P. Solodov, V. N. Temlyakov, S. Yu. Tikhonov, V. M. Fedorov, “Mikhail Konstantinovich Potapov (on his 90th birthday)”, Russian Math. Surveys, 76:2 (2021), 369–371  mathnet  crossref  crossref  isi
6. B. S. Kashin, Uspekhi Mat. Nauk, 2021  mathnet  crossref
7. Yuri V. Malykhin, “Kolmogorov Widths of the Besov Classes $B^1_{1,\theta }$ and Products of Octahedra”, Proc. Steklov Inst. Math., 312 (2021), 215–225  mathnet  crossref  crossref  isi  elib  scopus
8. T. I. Zaitseva, Yu. V. Malykhin, K. S. Ryutin, “On Recovery of Regular Ridge Functions”, Math. Notes, 109:2 (2021), 307–311  mathnet  crossref  crossref  mathscinet  isi  scopus
9. A.V. Shaposhnikov, “A note on Lusin-type approximation of Sobolev functions on Gaussian spaces”, Journal of Functional Analysis, 280:6 (2021) , arXiv: 1908.10183  crossref  isi  scopus
10. Vladimir I. Bogachev, Alexander Shaposhnikov, Feng-Yu Wang, “Sobolev-Kantorovich inequalities under $CD(0, \infty)$ condition”, Commun. Contemp. Math., 2021, 2150027–28 (Published online) , arXiv: 1603.07378  mathnet  crossref  scopus; (Published online)
11. Vladimir I. Bogachev, Egor D. Kosov, Alexander V. Shaposhnikov, “Regularity of solutions to Kolmogorov equations with perturbed drifts”, Potential Anal., 2021, 1–22 (Published online) , arXiv: 2104.04674  mathnet  crossref  isi  scopus; (Published online)
12. Nicola Gigli, Alexander Tyulenev, “Korevaar–Schoen's directional energy and Ambrosio's regular Lagrangian flows”, Math. Z., 298 (2021), 1221–1261 , arXiv: 1901.03564  mathnet  crossref  isi  scopus;
13. A. I. Tyulenev, Almost sharp descriptions of traces of Sobolev $W_{p}^{1}(\mathbb{R}^{n})$-spaces to arbitrary compact subsets of $\mathbb{R}^{n}$. The case $p \in (1,n]$, 2021 , 67 pp., arXiv: 2109.07553
14. Nicola Gigli, Alexander Tyulenev, “Korevaar–Schoen's energy on strongly rectifiable spaces”, Calc. Var. Partial Differential Equations, 60 (2021), 235 , 54 pp., arXiv: 2002.07440  mathnet  crossref  isi  scopus;

   2020
15. D. S. Telyakovskii, S. A. Telyakovskii, “Geometric approach to finding the conditional extrema”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 4, 2020, 244–254  mathnet  crossref  isi  elib  scopus
16. O. V. Besov, Dokl. RAN. Math. Inf. Proc. upr., 491:1 (2020), 11–14  mathnet  crossref  isi  elib
17. O. V. Besov, “Multiplicative Estimates for Derivatives on a Domain”, Math. Notes, 108:4 (2020), 492–498  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
18. O. V. Besov, “Interpolation of spaces of functions of positive smoothness on a domain”, Dokl. RAN. Math. Inf. Proc. upr., 495:1 (2020), 8–12  mathnet  crossref  isi  elib
19. B. S. Kashin, I. V. Limonova, “Weakly Lacunary Orthogonal Systems and Properties of the Maximal Partial Sum Operator for Subsystems”, Proc. Steklov Inst. Math., 311 (2020), 152–170  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
20. B. S. Kashin, “Remarks on the Uniform and Absolute Convergence of Orthogonal Series”, Math. Notes, 108:5 (2020), 744–748  mathnet  crossref  crossref  isi  elib  scopus
21. S. V. Bolotin, A. V. Borisov, A. V. Karapetyan, B. S. Kashin, E. I. Kugushev, A. I. Neishtadt, D. O. Orlov, D. V. Treschev, “Valerii Vasil'evich Kozlov (on his 70th birthday)”, Russian Math. Surveys, 75:6 (2020), 1165–1180  mathnet  crossref  crossref  isi
22. Yu. V. Malykhin, E. V. Shchepin, Dokl. RAN. Math. Inf. Proc. upr., 491:1 (2020), 68–72  mathnet  crossref  isi  elib
23. A.V. Shaposhnikov, L. Wresch, Pathwise vs. path-by-path uniqueness, 2020 , 14 pp., arXiv: 2001.02869v3
24. S. K. Vodopyanov, A. I. Tyulenev, “Sobolev $W^1_p$-spaces on $d$-thick closed subsets of $\mathbb R^n$”, Sb. Math., 211:6 (2020), 786–837  mathnet  crossref  crossref  mathscinet  isi  elib  scopus

   2019
25. O. V. Besov, “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains”, Math. Notes, 106:4 (2019), 501–513  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
26. O. V. Besov, “Embeddings of spaces of functions of positive smoothness on irregular domains”, Dokl. Math., 99:1 (2019), 31–35  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
27. A. I. Aptekarev, A. M. Akhtyamov, O. V. Besov, A. A. Vladimirov, B. S. Kashin, K. A. Mirzoev, S. N. Naboko, R. O. Oinarov, I. V. Sadovnichaya, A. M. Savchuk, A. G. Sergeev, V. D. Stepanov, Ya. T. Sultanaev, D. V. Treschev, I. A. Sheipak, “Andrei Andreevich Shkalikov (on his seventieth birthday)”, Trans. Moscow Math. Soc., 80 (2019), 113–122  mathnet  crossref  elib  scopus
28. V. A. Sadovnichii, V. N. Chubarikov, B. S. Kashin, V. V. Vlasov, V. V. Galatenko, V. E. Podolskii, T. V. Rodionov, V. A. Skvortsov, A. P. Solodov, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019, no. 2, 70–71  mathnet
29. B. S. Kashin, I. V. Limonova, “Decomposing a Matrix into two Submatrices with Extremally Small (2,1)-Norm”, Math. Notes, 106:1 (2019), 63–70  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  hlocal  elib  scopus (cited: 1)
30. V. I. Bogachev, I. V. Volovich, B. S. Kashin, V. V. Kozlov, V. P. Maslov, V. A. Sadovnichii, A. M. Stepin, V. M. Tikhomirov, A. Yu. Khrennikov, E. T. Shavgulidze, “Oleg Georgievich Smolyanov (on his 80th birthday)”, Russian Math. Surveys, 74:4 (2019), 771–773  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
31. B. S. Kashin, I. V. Limonova, “Selecting a dense weakly lacunary subsystem in a bounded orthonormal system”, Russian Math. Surveys, 74:5 (2019), 956–958  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  scopus (cited: 1)
32. V.I. Bogachev, A.V. Shaposhnikov, S.V. Shaposhnikov, “Log-Sobolev-type inequalities for solutions to stationary Fokker-Planck-Kolmogorov equations”, Calculus of Variations and Partial Differential Equations, 2019, no. 58, 176 , 16 pp., arXiv: 1805.09467  crossref  isi  scopus

   2018
33. S. A. Telyakovskii, “On the Convergence of Block Fourier Series of Functions of Bounded Variation in Two Variables”, Math. Notes, 103:4 (2018), 645–648  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  scopus (cited: 1)
34. O. V. Besov, “Embeddings of Weighted Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Space”, Math. Notes, 104:6 (2018), 799–809  mathnet  crossref  crossref  mathscinet  mathscinet  zmath  isi (cited: 2)  elib  elib  scopus (cited: 2)
35. O. V. Besov, “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Spaces”, Math. Notes, 103:3 (2018), 348–356  mathnet  crossref  crossref  mathscinet  isi (cited: 5)  elib  scopus (cited: 5)
36. Math. Notes, 103:5 (2018), 865  mathnet  crossref  mathscinet  isi  elib  scopus
37. O. V. Besov, “Embeddings for Weighted Spaces of Functions of Positive Smoothness on Irregular Domains into Lebesgue Spaces”, Dokl. Math., 97:3 (2018), 236–239  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus
38. S. V. Bochkarev, “An abstract Kolmogorov theorem, and an application to metric spaces and topological groups”, Sb. Math., 209:11 (2018), 1575–1602  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
39. Garmonicheskii analiz, teoriya priblizhenii i teoriya chisel, Sbornik statei. K 60-letiyu so dnya rozhdeniya akademika Sergeya Vladimirovicha Konyagina, Trudy MIAN, 303, ed. B. S. Kashin, Yu. V. Malykhin, V. Yu. Protasov, I. D. Shkredov, K. S. Ryutin, MAIK Nauka/Interperiodika, M., 2018 , 287 pp.  mathnet
40. A. I. Aptekarev, V. M. Buchstaber, V. A. Vassiliev, M. L. Gromov, Yu. S. Ilyashenko, B. S. Kashin, V. M. Keselman, V. V. Kozlov, M. L. Kontsevich, I. M. Krichever, N. G. Kruzhilin, S. K. Lando, Yu. I. Manin, G. A. Margulis, S. Yu. Nemirovski, S. P. Novikov, Yu. G. Reshetnyak, Ya. G. Sinai, S. P. Suetin, D. V. Treschev, D. B. Fuchs, A. G. Khovanskii, E. M. Chirka, A. S. Schwarz, A. N. Shiryaev, “Vladimir Antonovich Zorich (on his 80th birthday)”, Russian Math. Surveys, 73:5 (2018), 935–939  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
41. B. S. Kashin, Yu. V. Malykhin, K. S. Ryutin, “Kolmogorov width and approximate rank”, Proc. Steklov Inst. Math., 303 (2018), 140–153  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  hlocal  elib  scopus (cited: 1)
42. B. I. Golubov, B. S. Kashin, L. Yu. Kossovich, S. P. Sidorov, A. P. Khromov, A. N. Chumachenko, “19th International Saratov Winter School Contemporary problems of function theory and their applications"”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 18:3 (2018), 354–365  mathnet  mathscinet
43. B. S. Kashin, Yu. V. Malykhin, V. Yu. Protasov, K. S. Ryutin, I. D. Shkredov, “Sergei Vladimirovich Konyagin turns 60”, Proc. Steklov Inst. Math., 303 (2018), 1–9  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
44. B. S. Kashin, V. N. Temlyakov, “Observations on discretization of trigonometric polynomials with given spectrum”, Russian Math. Surveys, 73:6 (2018), 1128–1130  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 5)  hlocal  elib  scopus (cited: 5)

   2017
45. O. V. Besov, “Another Note on the Embedding of the Sobolev Space for the Limiting Exponent”, Math. Notes, 101:4 (2017), 608–618  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  scopus (cited: 1)
46. B. S. Kashin, A. V. Meleshkina, “Letter to the Editor”, Math. Notes, 101:4 (2017), 751  mathnet  crossref  crossref  mathscinet  isi  hlocal  elib  scopus
47. B. S. Kashin, “Decomposing an orthogonal matrix into two submatrices with extremally small $(2,1)$-norm”, Russian Math. Surveys, 72:5 (2017), 971–973  mathnet  crossref  crossref  mathscinet  mathscinet  adsnasa  isi (cited: 1)  hlocal  elib  scopus
48. Yu. V. Malykhin, K. S. Ryutin, “The Product of Octahedra is Badly Approximated in the $\ell_{2,1}$-Metric”, Math. Notes, 101:1 (2017), 94–99 , arXiv: 1606.00738  mathnet  crossref  crossref  mathscinet  isi (cited: 6)  elib  elib  scopus (cited: 4)
49. Yu. V. Malykhin, E. V. Shchepin, “Chain development of metric compacts”, Topology Appl., 221 (2017), 624–629 , arXiv: 1604.00848  mathnet  crossref  mathscinet  isi (cited: 1)  elib  scopus (cited: 1)
50. E. S. Belkina, Y. V. Malykhin, “Fourier coefficients of continuous functions with respect to localized Haar system”, Probl. anal. Issues Anal., 6(24):1 (2017), 11–18  mathnet  crossref  mathscinet  isi  elib  scopus
51. A.V. Shaposhnikov, Correction to the paper “Some remarks on Davies uniqueness theorem”, 2017 , 7 pp., arXiv: 1703.06598
52. A. I. Tyulenev, “On various approaches to Besov-type spaces of variable smoothness”, J. Math. Anal. Appl., 451:1 (2017), 371–392  mathnet  crossref  mathscinet  isi (cited: 4)  elib  scopus (cited: 4)
53. A. I. Tyulenev, S. K. Vodop'yanov, “On the Whitney Problem for Weighted Sobolev Spaces”, Dokl. Math., 95:1 (2017), 79–83  mathnet  crossref  crossref  mathscinet  isi  elib  scopus  scopus

   2016
54. S. A. Telyakovskii, “On the Rate of Convergence in $L$ of Fourier Sine Series with Monotone Coefficients”, Math. Notes, 100:3 (2016), 472–476  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib  elib  scopus (cited: 2)

   2018
55. Yu. N. Subbotin, S. A. Telyakovskii, “Uniform approximation of curvature of smooth planar curves”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 184–186  mathnet  crossref  crossref  mathscinet  isi  elib  scopus

   2016
56. O. V. Besov, “Spaces of functions of positive smoothness on irregular domains”, Dokl. Math., 93:1 (2016), 13–15  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 7)  elib  elib  scopus (cited: 2)
57. Funktsionalnye prostranstva, teoriya priblizhenii, smezhnye razdely matematicheskogo analiza, Sbornik statei. K 110-letiyu so dnya rozhdeniya akademika Sergeya Mikhailovicha Nikolskogo, Trudy MIAN, 293, ed. O. V. Besov, A. G. Sergeev, MAIK Nauka/Interperiodika, M., 2016 , 351 pp.  mathnet
58. O. V. Besov, “Spaces of functions of positive smoothness on irregular domains”, Proc. Steklov Inst. Math., 293 (2016), 56–66  mathnet  crossref  crossref  mathscinet  isi (cited: 6)  elib  elib  scopus (cited: 4)
59. M. V. Balashov, O. V. Besov, B. I. Golubov, V. V. Goryainov, V. N. Diesperov, S. I. Dudov, G. E. Ivanov, S. P. Konovalov, R. V. Konstantinov, A. B. Kurzhanskii, S. R. Nasyrov, A. G. Sergeev, V. V. Starkov, V. M. Tikhomirov, M. I. Shabunin, “Evgenii Sergeevich Polovinkin (on his 70th birthday)”, Russian Math. Surveys, 71:5 (2016), 983–987  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
60. O.V. Besov, Lektsii po matematicheskomu analizu, 3-e izd., Fizmatlit, M., 2016 , 480 pp.
61. O. V. Besov, “Embedding of Sobolev spaces with limit exponent revisited”, Dokl. Math., 94:3 (2016), 684–687  mathnet  crossref  crossref  isi  elib  elib  scopus
62. B. I. Golubov, B. S. Kashin, T. P. Lukashenko, M. G. Plotnikov, M. A. Skopina, A. P. Solodov, A. M. Stepin, N. N. Kholshchevnikova, “Valentin Anatol'evich Skvortsov (on his 80th birthday)”, Russian Math. Surveys, 71:1 (2016), 175–177  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
63. B. I. Golubov, B. S. Kashin, L. Yu. Kossovich, S. P. Sidorov, A. P. Khromov, A. N. Chumachenko, “18th International Saratov Winter School “Contemporary Problems of Function Theory and Their Applications””, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 16:4 (2016), 485–487  mathnet
64. B. S. Kashin, “Dyadic analogues of Hilbert matrices”, Russian Math. Surveys, 71:6 (2016), 1135–1136  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 4)  hlocal  elib  elib  scopus (cited: 2)
65. B. Kashin, P. Nevai, S. Suetin, V. Totik, “Special Issue Dedicated to the memory of Andrei Aleksandrovich Gonchar and Herbert Stahl”, J. Approx. Theory, 206, Special Issue (2016), IV  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
66. E. A. Volkov, A. A. Dosiyev, “On the numerical solution of a multilevel nonlocal problem”, Mediterr. J. Math., 13:5 (2016), 3589–3604  mathnet  crossref  mathscinet  zmath  isi (cited: 5)  elib  scopus (cited: 5)
67. Yu. V. Malykhin, “Relative widths of Sobolev classes in the uniform and integral metrics”, Proc. Steklov Inst. Math., 293 (2016), 209–215  mathnet  crossref  crossref  mathscinet  isi (cited: 3)  elib  elib  scopus (cited: 2)
68. A.V. Shaposhnikov, “Some Remarks on Davies Uniqueness Theorem”, Proceedings of the Edinburgh Mathematical Society, 59:4 (2016), 1019-1035 , arXiv: 1401.5455  crossref  isi (cited: 7)  scopus (cited: 7)
69. A. I. Tyulenev, “Besov-type spaces of variable smoothness on rough domains”, Nonlinear Anal., 145 (2016), 176–198  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  elib  scopus (cited: 3)

   2015
70. Yu. N. Subbotin, S. A. Telyakovskii, “On the Norms of Favard Kernels”, Math. Notes, 97:4 (2015), 598–604  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
71. S. A. Telyakovskii, “On the Coefficients of Fourier Series Convergent in $L$”, Math. Notes, 98:1 (2015), 189–191  mathnet  crossref  crossref  mathscinet  isi  elib  elib  scopus (cited: 1)
72. Yu. V. Malykhin, S. A. Telyakovskii, N. N. Kholshchevnikova, “Integrability of the Sum of Absolute Values of Blocks of the Fourier–Walsh Series for Functions of Bounded Variation”, Proc. Steklov Inst. Math., 290 (2015), 306–317  mathnet  crossref  crossref  isi (cited: 2)  elib  elib  scopus (cited: 2)

   2017
73. S. A. Telyakovskii, “An addition to V.P. Zastavnyi's paper “Estimates for sums of moduli of blocks in trigonometric Fourier series””, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 186–190  mathnet  crossref  mathscinet  isi (cited: 1)  elib  scopus (cited: 1)

   2015
74. S. A. Telyakovskii, “O svoistvakh ryadov iz modulei blokov trigonometricheskogo ryada”, Materialy mezhdunarodnoi nauchnoi konferentsii «Teoriya priblizhenii funktsii i rodstvennye zadachi analiza», posvyaschennoi pamyati doktora fiziko-matematicheskikh nauk, professora P. P. Korovkina (Kaluga, 09–10 oktyabrya 2015 g.), Izd-vo Kaluzhskogo gosudarstvennogo universiteta imeni K. E. Tsiolkovskogo, Kaluga, 2015, 71–72  elib
75. O. V. Besov, Lektsii po matematicheskomu analizu, 2-e izd., ispravlennoe i dopolnennoe, FIZMATLIT, M., 2015 , 480 pp.
76. O. V. Besov, “Embeddings of Sobolev spaces in the case of the limit exponent”, Dokl. Math., 91:3 (2015), 277–280  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus (cited: 1)
77. O. V. Besov, “Embedding of a Weighted Sobolev Space and Properties of the Domain”, Proc. Steklov Inst. Math., 289 (2015), 96–103  mathnet  crossref  crossref  isi (cited: 6)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 3)
78. O. V. Besov, “Embedding of Sobolev Space in the Case of the Limit Exponent”, Math. Notes, 98:4 (2015), 550–560  mathnet  crossref  crossref  mathscinet  isi (cited: 3)  elib  elib  scopus (cited: 1)
79. S. V. Bochkarev, “Kolmogorovs abstract theorem: Application to metric spaces and topological groups”, Dokl. Math., 91:3 (2015), 367–370  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus (cited: 1)
80. B. S. Kashin, “Lunin's method for selecting large submatrices with small norm”, Sb. Math., 206:7 (2015), 980–987  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 7)  hlocal  elib  elib  scopus (cited: 3)
81. B. I. Golubov, B. S. Kashin, L. Yu. Kossovich, S. P. Sidorov, A. P. Khromov, “XVII International Saratov Winter School <Contemporary Problems of the Function Theory and its Applications>. Dedicated to the 150th Anniversary of V.  A. Steklov”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 15:3 (2015), 357–359  mathnet  elib
82. V. M. Buchstaber, V. N. Dubinin, V. A. Kaliaguine, B. S. Kashin, V. N. Sorokin, S. P. Suetin, D. N. Tulyakov, B. N. Chetverushkin, E. M. Chirka, A. A. Shkalikov, “Alexander Ivanovich Aptekarev (on his 60th birthday)”, Russian Math. Surveys, 70:5 (2015), 965–973  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
83. B. Kashin, P. Nevai, S. Suetin, V. Totik, “Special Issue Dedicated to the memory of Andrei Aleksandrovich Gonchar and Herbert Stahl”, J. Approx. Theory, 190, Special Issue (2015), III  crossref  mathscinet  zmath  isi  scopus
84. M. I. Zelikin, A. O. Ivanov, B. S. Kashin, A. S. Mishchenko, Yu. V. Nesterenko, A. A. Oshemkov, F. Yu. Popelenskii, V. A. Sadovnichii, A. A. Tuzhilin, V. N. Chubarikov, A. I. Shafarevich, A. N. Shiryaev, “Academician Anatolii Timofeevich Fomenko”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 6, 66–68  mathnet
85. Yu. V. Malykhin, E. V. Shchepin, “Chain Development”, Proc. Steklov Inst. Math., 290 (2015), 300–305  mathnet  crossref  crossref  isi (cited: 1)  elib  elib  scopus (cited: 1)
86. A. I. Tyulenev, “Some new function spaces of variable smoothness”, Sb. Math., 206:6 (2015), 849–891  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 9)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 8)
87. A. I. Tyulenev, “Traces of weighted Sobolev spaces with Muckenhoupt weight. The case $p=1$”, Nonlinear Anal., 128 (2015), 248–272  mathnet  crossref  mathscinet  isi (cited: 9)  elib  scopus (cited: 9)
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