Persons: Kalyabin, Gennadiy Anatolievich

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Kalyabin, Gennadiy Anatolievich

Professor

Doctor of physico-mathematical sciences (1981)

Speciality:

01.01.01 (Real analysis, complex analysis, and functional analysis)

E-mail:

Keywords:

function spaces; embedding theorems; approximation, extension and decomposition; operator theory; matrix theory. Ramanujan-Robin inequality

UDC:

517.518.26, 517.518.237, 517.518.118, 51, 511.216, 511.3357.518.826, 517.518.83, 512.643.5, 513.881, 517.51, 517.518, 517, 517.5, 517.518.22, 517.518.23, 517.927

MSC:

46E35, 15A18, 46E20,

Subject:

analysis

Main publications:

Kalyabin G. A., Lizorkin P. I. Spaces of functions of generalized smoothness // Mathematische Nachrichten, v. 133, 1987, p. 7–32.
Kalyabin G. A. Asymptotic formula for minimal eigenvalues of Hilbert type matrices // Proceedings of the Second ISAAC Congress, Kluwer Academic Publishers, DORDRECHT/BOSTON/LONDON, v. 2, 2000, p. 1155–1162.

https://www.mathnet.ru/eng/person17646

List of publications on Google Scholar

https://zbmath.org/authors/ai:kalyabin.gennadiy-a

https://mathscinet.ams.org/mathscinet/MRAuthorID/195857

https://elibrary.ru/author_items.asp?authorid=4666

https://www.scopus.com/authid/detail.url?authorId=6602429768

	Publications in Math-Net.Ru	Citations
	2014
1.	G. A. Kalyabin, “On two-sided and asymptotic estimates for the norms of embedding operators of $\mathring W_2^n(-1,1)$ into $L_q(d\mu)$”, Trudy Mat. Inst. Steklova, 284 (2014), 169–175 ; Proc. Steklov Inst. Math., 284 (2014), 161–167
	2013
2.	G. A. Kalyabin, “New examples of Pompeiu functions”, Eurasian Math. J., 4:3 (2013), 63–69
	2011
3.	G. A. Kalyabin, “Sharp Constants in One-Dimensional Poincaré-Type Inequalities”, Mat. Zametki, 90:4 (2011), 634–636 ; Math. Notes, 90:4 (2011), 615–618
	2010
4.	G. A. Kalyabin, “Sharp estimates for derivatives of functions in the Sobolev classes $\mathring W_2^r(-1,1)$”, Trudy Mat. Inst. Steklova, 269 (2010), 143–149 ; Proc. Steklov Inst. Math., 269 (2010), 137–142	10
	2007
5.	G. A. Kalyabin, “A NonDensity Criterion for $L^\infty(\mathbb R^n)$ in $L^{p(\cdot)}(\mathbb R^n)$”, Mat. Zametki, 82:2 (2007), 315–316 ; Math. Notes, 82:2 (2007), 277–278	2
	2006
6.	G. A. Kalyabin, “Some Problems for Sobolev Spaces on the Half-line”, Trudy Mat. Inst. Steklova, 255 (2006), 161–169 ; Proc. Steklov Inst. Math., 255 (2006), 150–158	6
	2005
7.	G. A. Kalyabin, “Effective Formulas for Constants in the Stechkin–Gabushin Problem”, Trudy Mat. Inst. Steklova, 248 (2005), 124–129 ; Proc. Steklov Inst. Math., 248 (2005), 118–124	3
	2004
8.	G. A. Kalyabin, “Sharp Constants in Inequalities for Intermediate Derivatives (the Gabushin Case)”, Funktsional. Anal. i Prilozhen., 38:3 (2004), 29–38 ; Funct. Anal. Appl., 38:3 (2004), 184–191	13
	2003
9.	G. A. Kalyabin, “Extrapolations with the Least Norms in the Sobolev Spaces $W_2^n$ on the Half-Axis and the Whole Axis”, Trudy Mat. Inst. Steklova, 243 (2003), 230–236 ; Proc. Steklov Inst. Math., 243 (2003), 220–226	1
	2002
10.	G. A. Kalyabin, “The Best Extension Operators for Sobolev Spaces on the Half-Line”, Funktsional. Anal. i Prilozhen., 36:2 (2002), 28–37 ; Funct. Anal. Appl., 36:2 (2002), 106–113	6
	2001
11.	G. A. Kalyabin, “An Asymptotic Formula for the Minimum Eigenvalues of Hilbert Type Matrices”, Funktsional. Anal. i Prilozhen., 35:1 (2001), 80–84 ; Funct. Anal. Appl., 35:1 (2001), 67–70	9
	1999
12.	G. A. Kalyabin, “Upper Estimates for the Coefficients of Algebraic Polynomials via Their $L_p$-Norms on Intervals”, Trudy Mat. Inst. Steklova, 227 (1999), 152–161 ; Proc. Steklov Inst. Math., 227 (1999), 146–154	2
13.	G. A. Kalyabin, “Bilateral Estimates for the Least Norm of Extension Operators from Plane Convex Domains for Sobolev Spaces”, Trudy Mat. Inst. Steklova, 227 (1999), 146–151 ; Proc. Steklov Inst. Math., 227 (1999), 140–145	2
	1995
14.	G. A. Kalyabin, “An effective description of the sum of some pairs of spaces of the Besov and Lizorkin–Triebel types”, Trudy Mat. Inst. Steklov., 210 (1995), 120–128 ; Proc. Steklov Inst. Math., 210 (1995), 89–95	1
	1993
15.	G. A. Kalyabin, “Two-sided estimates and exact values of some capacities”, Dokl. Akad. Nauk, 331:6 (1993), 672–673 ; Dokl. Math., 48:1 (1994), 192–194
16.	G. A. Kalyabin, “Pointwise multipliers in certain Sobolev spaces containing unbounded functions”, Trudy Mat. Inst. Steklov., 204 (1993), 160–165 ; Proc. Steklov Inst. Math., 204 (1994), 137–141	3
	1988
17.	G. A. Kalyabin, “Characterization of spaces of Besov–Lizorkin–Triebel type by means of generalized differences”, Trudy Mat. Inst. Steklov., 181 (1988), 95–116 ; Proc. Steklov Inst. Math., 181 (1989), 103–125	8
	1987
18.	G. A. Kalyabin, “On the moduli of smoothness of functions given on a sphere”, Dokl. Akad. Nauk SSSR, 294:5 (1987), 1051–1054	4
19.	G. A. Kalyabin, “Integral representations and estimates for generalized differences of entire functions of exponential type”, Trudy Mat. Inst. Steklov., 180 (1987), 129–130 ; Proc. Steklov Inst. Math., 180 (1989), 150–151
	1985
20.	G. A. Kalyabin, “Characterization of certain function spaces by means of generalized differences”, Dokl. Akad. Nauk SSSR, 284:6 (1985), 1305–1308
21.	G. A. Kalyabin, “Theorems on extension, multipliers and diffeomorphisms for generalized Sobolev–Liouville classes in domains with a Lipschitz boundary”, Trudy Mat. Inst. Steklov., 172 (1985), 173–186 ; Proc. Steklov Inst. Math., 172 (1987), 191–205	8
	1984
22.	G. A. Kalyabin, S. I. Pis'mennaya, “Description of traces of the functions whose derivatives are bounded with certain weights”, Mat. Zametki, 35:3 (1984), 357–368 ; Math. Notes, 35:3 (1984), 186–192	2
	1983
23.	G. A. Kalyabin, “Function classes of Lizorkin-Triebel type in domains with Lipschitzian boundary”, Dokl. Akad. Nauk SSSR, 271:4 (1983), 795–798
24.	G. A. Kalyabin, “Correction: “Descriptions of functions from classes of Besov–Lizorkin–Triebel type””, Trudy Mat. Inst. Steklov., 161 (1983), 226
25.	G. A. Kalyabin, “Estimates for the capacity of sets with respect to generalized Lizorkin–Triebel classes and weighted Sobolev classes”, Trudy Mat. Inst. Steklov., 161 (1983), 111–124 ; Proc. Steklov Inst. Math., 161 (1984), 119–133	1
	1981
26.	G. A. Kalyabin, “Criteria for the multiplicativity and for the imbedding into $C$ of Besov–Lizorkin–Triebel type spaces”, Mat. Zametki, 30:4 (1981), 517–526 ; Math. Notes, 30:4 (1981), 750–755	5
	1980
27.	G. A. Kalyabin, “The Dirichlet problem for some degenerate elliptic equations with boundary functions in $L_p^*$”, Dokl. Akad. Nauk SSSR, 251:2 (1980), 274–276
28.	G. A. Kalyabin, “Multiplicativity conditions for function spaces of Besov and Lizorkin–Triebel type”, Dokl. Akad. Nauk SSSR, 251:1 (1980), 25–26	2
29.	G. A. Kalyabin, “Descriptions of functions from classes of Besov–Lizorkin–Triebel type”, Trudy Mat. Inst. Steklov., 156 (1980), 82–109	9
	1979
30.	G. A. Kalyabin, “Description of traces for anisotropic spaces of Triebel–Lizorkin type”, Trudy Mat. Inst. Steklov., 150 (1979), 160–173 ; Proc. Steklov Inst. Math., 150 (1981), 169–183	5
	1978
31.	G. A. Kalyabin, “Trace spaces for generalized anisotropic Liouville classes”, Izv. Akad. Nauk SSSR Ser. Mat., 42:2 (1978), 305–314 ; Math. USSR-Izv., 12:2 (1978), 289–297	1
32.	G. A. Kalyabin, “A generalized trace method in the interpolation theory of Banach spaces”, Mat. Sb. (N.S.), 106(148):1(5) (1978), 85–93 ; Math. USSR-Sb., 34:5 (1978), 645–653
	1977
33.	G. A. Kalyabin, “Characterization of functions in spaces of Besov–Lizorkin–Triebel type”, Dokl. Akad. Nauk SSSR, 236:5 (1977), 1056–1059	1
34.	G. A. Kalyabin, “Imbedding theorems for generalized Besov and Liouville spaces”, Dokl. Akad. Nauk SSSR, 232:6 (1977), 1245–1248	1
35.	G. A. Kalyabin, “A trace problem for weighted anisotropic spaces of Liouville type”, Izv. Akad. Nauk SSSR Ser. Mat., 41:5 (1977), 1138–1160 ; Math. USSR-Izv., 11:5 (1977), 1085–1107	5
36.	G. A. Kalyabin, “Characterization of spaces of generalized Liouville differentiation”, Mat. Sb. (N.S.), 104(146):1(9) (1977), 42–48 ; Math. USSR-Sb., 33:1 (1977), 37–42	11
	1976
37.	G. A. Kalyabin, “Description of traces for functions in weighted classes of Liouville type”, Dokl. Akad. Nauk SSSR, 227:2 (1976), 284–287	1
38.	E. S. Birger, G. A. Kalyabin, “Theory of Weyl circles in the case of a nonselfadjoint system of second order differential equations”, Differ. Uravn., 12:9 (1976), 1531–1540	2
39.	G. A. Kalyabin, “Trace spaces for a certain family of periodic weight classes”, Trudy Mat. Inst. Steklov., 140 (1976), 169–180 ; Proc. Steklov Inst. Math., 140 (1979), 183–195	3
	1975
40.	G. A. Kalyabin, “Estimates for functions with a finite O. V. Besov seminorm”, Differ. Uravn., 11:4 (1975), 713–717
41.	G. A. Kalyabin, “Traces of functions with majorizable derivatives”, Mat. Zametki, 18:4 (1975), 499–506 ; Math. Notes, 18:4 (1975), 886–890	1
	1973
42.	G. A. Kalyabin, “A necessary and sufficient condition for the discreteness of the spectrum of a monomial operation in the matrix case”, Differ. Uravn., 9:5 (1973), 951–954
	1972
43.	G. A. Kalyabin, “On the number of solutions of a self-adjoint system of second-order differential equations in $L_2(0,\infty)$”, Funktsional. Anal. i Prilozhen., 6:3 (1972), 74–76 ; Funct. Anal. Appl., 6:3 (1972), 237–239	3

	1977
44.	G. A. Kalyabin, “Поправки к статье “Теоремы вложения для обобщенных пространств Бесова и Лиувилля” (ДАН, т. 232, № 6, 1977 г.)”, Dokl. Akad. Nauk SSSR, 237:4 (1977), 760

Presentations in Math-Net.Ru

1.	Diverse results concerning Besov and Sobolev spaces G. A. Kalyabin Conference on the Theory of Functions of Several Real Variables, dedicated to the 90th anniversary of O. V. Besov June 1, 2023 10:00
2.	Одношагово $G$-неулучшаемые числа G. A. Kalyabin Contemporary Problems in Number Theory November 22, 2018 12:45
3.	О гипотезе Кэйвни-Николя-Сандоу G. A. Kalyabin Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics April 20, 2016 17:00
4.	On two S. M. Nikol'skii problems G. Kalyabin International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii May 27, 2015 15:45
5.	О функциях с разностями из $L_{p}((0,1)^{n})$ G. A. Kalyabin Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics November 12, 2014 16:00
6.	Об одном вопросе Отелбаева и Нурсултанова G. A. Kalyabin Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics November 16, 2011 16:00
7.	Обзор некоторых докладов на конференции "Гладкость, приближение, функциональные пространства - 2010", Йена (Германия) G. A. Kalyabin Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics December 1, 2010 16:00
8.	Экстремальные сплайны в неравенствах Маркова–Фридрихса–Колмогорова G. A. Kalyabin Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics May 12, 2010 16:00

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