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### Department of Function Theory

| Seminars | History of the Department | Research Fields | Awards | Publications |
Staff
 Besov Oleg Vladimirovich Doctor Phys.-Math. Sci., Corresponding Member of RAS, Head of Department, Chief Scientific Researcher office: 519; tel.: +7 (499) 941 01 89, +7 (495) 984 81 41 * 36 67; e-mail: besov@mi.ras.ruPersonal page: http://www.mi.ras.ru/~besov/ Principal fields of research: Functional spaces. Imbeddings. Approximation of classes of functions. List of publications Bochkarev Sergei Viktorovich Doctor Phys.-Math. Sci., Leading Scientific Researcher office: 503; tel.: +7 (495) 984 81 41 * 37 89; e-mail: bochkarv@mi.ras.ruPrincipal fields of research: Trigonometric and orthogonal series. Functional spaces. Bases and almost everywhere convergence. List of publications Kashin Boris Sergeevich Doctor Phys.-Math. Sci., Professor, Academician of RAS, Chief Scientific Researcher office: 517; tel.: +7 (495) 984 81 41 * 37 84; e-mail: kashin@mi.ras.ruPersonal page: http://www.mi.ras.ru/~kashin List of publications 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 List of publications Telyakovskii Sergei Aleksandrovich Doctor Phys.-Math. Sci., Professor, Leading Scientific Researcher office: 502; tel.: +7 (495) 984 81 41 * 37 88, +7 (495) 984 81 41 * 36 64; e-mail: SergeyAltel@yandex.ruPrincipal fields of research: Approximations of functions. Special trigonometric series. Extreme properties. Functions with bounded variation.Widths. List of publications 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 List of publications Volkov Evgenii Alekseevich Doctor Phys.-Math. Sci., Leading Scientific Researcher office: 502; tel.: +7 (495) 984 81 41 * 37 88, +7 (495) 984 81 41 * 36 64; 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. List of publications Golovko Andrei Yur'evich Scientific Researcher e-mail: andrewgolovko@yandex.ru List of publications Kuleshov Aleksandr Andreevich Candidate Phys.-Math. Sci., Senior Scientific Researcher e-mail: kuleshov.a.a@yandex.ru List of publications Meleshkina Anna Vladimirovna Scientific Researcher e-mail: meleshkina-anna@mail.ru List of publications Radomskii Artyom Olegovich Candidate Phys.-Math. Sci., Senior Scientific Researcher e-mail: artrad@list.ru List of publications Shteinikov Yurii Nikolaevich Candidate Phys.-Math. Sci., Senior Scientific Researcher e-mail: g123g@yandex.ru List of publications Vasil'eva Anastasia Andreevna Doctor Phys.-Math. Sci., Senior Scientific Researcher e-mail: vasilyeva_nastya@inbox.ru List of publications Burenkov Viktor Ivanovich Doctor Phys.-Math. Sci., Professor, Out-Of-Staff Member e-mail: burenkov@cardiff.ac.ukPersonal page: http://www.enu.kz/ru/lica-enu/burenkov-viktor-ivanovich/ List of publications Oskolkov Konstantin Il'ich Doctor Phys.-Math. Sci., Professor, Out-Of-Staff Member e-mail: oskolkov@math.sc.eduPersonal page: http://www.math.sc.edu/konstantin-oskolkov Stepanov Vladimir Dmitrievich Doctor Phys.-Math. Sci., Professor, Corresponding Member of RAS, Out-Of-Staff Member e-mail: stepanov@mi.ras.ru List of publications Temlyakov Vladimir Nikolaevich Doctor Phys.-Math. Sci., Professor, Out-Of-Staff Member e-mail: temlyak@math.sc.eduPersonal page: http://www.math.sc.edu/people/temlyakov.html List of publications 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. List of publications 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. List of publications Pokhozhaev Stanislav Ivanovich (24.08.1935 – 30.01.2014) Doctor Phys.-Math. Sci., Professor, Corresponding Member of RAS Personal page: http://www.mi.ras.ru/~pokhozhaev Principal fields of research: Nonlinear functional analysis. Nonlinear PDE's. Nonlinear variational problems. List of publications
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Seminars
 Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics Seminar Chairman: O. V. Besov Steklov Mathematical Institute, Room 530 (8 Gubkina) Seminar on Approximation Theory Seminar Chairman: 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 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 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 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 Correspondent Member of Academy O. V. Besov is the Head of the Department. At present the staff of the department includes Academician B. S. Kashin, Correspondent Members of Academy S. V. Konyagin, S. I. Pokozhaev, Doctors of Phys.-Math. Sci. S. V. Bochkarev, E. A. Volkov, S. A. Telyakovskii, 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. At different 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 State Prize of Ukraine (1994);
The Kolmogorov Prize (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
 | by years | scientific publications | by types |

 2018 1. 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 2. O. V. Besov, “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Spaces”, Math. Notes, 103:3 (2018), 348–356 3. Math. Notes, 103:5 (2018), 865 4. A. A. Vasil'eva, “Entropy Numbers of Embeddings of Function Spaces on Sets with Tree-Like Structure: Some Generalized Limiting Cases”, Russian Journal of Mathematical Physics, 25:2 (2018), 248–270 (to appear) 5. S. V. Konyagin, A. A. Kuleshov, V. E. Maiorov, Complex analysis, mathematical physics, and applications, Collected papers, Tr. Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018 (to appear) 2017 6. O. V. Besov, “Another Note on the Embedding of the Sobolev Space for the Limiting Exponent”, Math. Notes, 101:4 (2017), 608–618 7. A. A. Vasil'eva, “Entropy numbers of embedding operators of function spaces on sets with tree-like structure”, Izv. Math., 81:6 (2017), 1095–1142                 (cited: 1) 8. A. A. Vasil'eva, “Widths of weighted Sobolev classes with constraints $f(a)=\dots=f^{(k-1)}(a)=f^{(k)}(b)=\dots=f^{(r-1)}(b)=0$ and the spectra of nonlinear differential equations”, Russ. J. Math. Phys., 24:3 (2017), 376–398 9. A. A. Vasil'eva, “Estimates for the Kolmogorov widths of weighted Sobolev classes on a domain with cusp: case of weights that are functions of the distance from the boundary”, Eurasian Math. J., 8:4 (2017), 102–106 10. B. S. Kashin, A. V. Meleshkina, “Letter to the Editor”, Math. Notes, 101:4 (2017), 751 11. B. S. Kashin, “Decomposing an orthogonal matrix into two submatrices with extremally small $(2,1)$-norm”, Russian Math. Surveys, 72:5 (2017), 971–973 12. 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           (cited: 2)     (cited: 1) 13. Yu. V. Malykhin, E. V. Shchepin, “Chain development of metric compacts”, Topology Appl., 221 (2017), 624–629 , arXiv: 1604.00848       (cited: 1)   (cited: 1) 14. 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 15. A. O. Radomskii, “On a Sidon-type Inequality for Discrete Orthonormal Systems”, Math. Notes, 101:4 (2017), 693–698 16. A. O. Radomskii, “On an inequality of Sidon for trigonometric polynomials”, Algebra i Analiz, 29:4 (2017), 140–158 17. Yu. N. Shteinikov, “Addendum to J. Cilleruelo, D.S. Ramana, and O. Ramaré's Paper “Quotient and Product Sets of Thin Subsets of the Positive Integers””, Proc. Steklov Inst. Math., 296 (2017), 251–255           (cited: 2) 18. Yu. N. Shteinikov, “On the product sets of rational numbers”, Proc. Steklov Inst. Math., 296 (2017), 243–250           (cited: 2)     (cited: 2)   (cited: 2) 19. Yu. N. Shteinikov, “Character sums over shifted powers”, Chebyshevskii sb., 18:2 (2017), 247–254 20. A. I. Tyulenev, “On various approaches to Besov-type spaces of variable smoothness”, J. Math. Anal. Appl., 451:1 (2017), 371–392         (cited: 1) 21. A. I. Tyulenev, S. K. Vodop'yanov, “On the Whitney Problem for Weighted Sobolev Spaces”, Dokl. Math., 95:1 (2017), 79–83 22. A. A. Kuleshov, “Continuous Sums of Ridge Functions on a Convex Body and the Class VMO”, Math. Notes, 102:6 (2017), 799–805 2016 23. S. A. Telyakovskii, “On the Rate of Convergence in $L$ of Fourier Sine Series with Monotone Coefficients”, Math. Notes, 100:3 (2016), 472–476 2018 24. 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 2016 25. O. V. Besov, “Spaces of functions of positive smoothness on irregular domains”, Dokl. Math., 93:1 (2016), 13–15             (cited: 4)       (cited: 1) 26. Funktsionalnye prostranstva, teoriya priblizhenii, smezhnye razdely matematicheskogo analiza, Sbornik statei. K 110-letiyu so dnya rozhdeniya akademika Sergeya Mikhailovicha Nikolskogo, Tr. MIAN, 293, ed. O. V. Besov, A. G. Sergeev, MAIK «Nauka/Interperiodika», M., 2016 , 351 pp. 27. O. V. Besov, “Spaces of functions of positive smoothness on irregular domains”, Proc. Steklov Inst. Math., 293 (2016), 56–66           (cited: 3)       (cited: 1) 28. 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 29. O.V. Besov, Lektsii po matematicheskomu analizu, 3-e izd., Fizmatlit, M., 2016 , 480 pp. 30. O. V. Besov, “Embedding of Sobolev spaces with limit exponent revisited”, Dokl. Math., 94:3 (2016), 684–687 31. Math. Notes, 99:2 (2016), 243–252           (cited: 1)     (cited: 1) 32. A. A. Vasil'eva, “Estimates for the entropy numbers of embedding operators of function spaces on sets with tree-like structure: Some limiting cases”, J. Complexity, 36 (2016), 74–105                 (cited: 1) 33. A. A. Vasil'eva, “Estimates for the widths of discrete function classes generated by a two-weight summation operator”, Proc. Steklov Inst. Math., 294 (2016), 291–307           (cited: 1)       (cited: 1) 34. A. A. Vasil'eva, “Embedding theorems for a weighted Sobolev class in the space $L_{q,v}$ with weights having a singularity at a point: Case $v\notin L_q$”, Russ. J. Math. Phys., 23:3 (2016), 392–424 35. 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 36. 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 37. B. S. Kashin, “Dyadic analogues of Hilbert matrices”, Russian Math. Surveys, 71:6 (2016), 1135–1136 38. 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     (cited: 1) 39. E. A. Volkov, A. A. Dosiyev, “On the numerical solution of a multilevel nonlocal problem”, Mediterr. J. Math., 13:5 (2016), 3589–3604               (cited: 1) 40. Yu. V. Malykhin, “Relative widths of Sobolev classes in the uniform and integral metrics”, Proc. Steklov Inst. Math., 293 (2016), 209–215           (cited: 2)       (cited: 1) 41. A. V. Meleshkina, “Absolute convergence of Fourier series in bounded complete double orthonormal systems”, Russian Math. Surveys, 71:2 (2016), 379–381 42. A. O. Radomskii, “On nonequivalence of the $\mathrm{C}$- and $\mathrm{QC}$-norms in the space of trigonometric polynomials”, Sb. Math., 207:12 (2016), 1729–1742 43. Yu. N. Shteinikov, “On the distribution of elements semigroups of natural numbers II”, Chebyshevskii Sb., 17:3 (2016), 197–203 44. A. I. Tyulenev, “Besov-type spaces of variable smoothness on rough domains”, Nonlinear Anal., 145 (2016), 176–198           (cited: 2)     (cited: 3) 45. A. I. Tyulenev, S. K. Vodop'yanov, On a Whitney-type problem for weighted Sobolev spaces on $d$-thick closed sets, 2016 , arXiv: 1606.06749 46. S. V. Konyagin, A. A. Kuleshov, “On some properties of finite sums of ridge functions defined on convex subsets of $\mathbb R^n$”, Proc. Steklov Inst. Math., 293 (2016), 186–193           (cited: 3)       (cited: 1) 47. A. A. Kuleshov, “On some properties of smooth sums of ridge functions”, Proc. Steklov Inst. Math., 294 (2016), 89–94           (cited: 1) 2015 48. Yu. N. Subbotin, S. A. Telyakovskii, “On the Norms of Favard Kernels”, Math. Notes, 97:4 (2015), 598–604 49. S. A. Telyakovskii, “On the Coefficients of Fourier Series Convergent in $L$”, Math. Notes, 98:1 (2015), 189–191 50. 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         (cited: 1)       (cited: 1) 2017 51. 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 2015 52. 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 53. O. V. Besov, Lektsii po matematicheskomu analizu, 2-e izd., ispravlennoe i dopolnennoe, FIZMATLIT, M., 2015 , 480 pp. 54. O. V. Besov, “Embeddings of Sobolev spaces in the case of the limit exponent”, Dokl. Math., 91:3 (2015), 277–280 55. O. V. Besov, “Embedding of a Weighted Sobolev Space and Properties of the Domain”, Proc. Steklov Inst. 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