Persons: Golubov, Boris Ivanovich

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Golubov, Boris Ivanovich

Statistics Math-Net.Ru
Total publications:	71
Scientific articles:	60
Presentations:	3

Number of views:
This page:	5925
Abstract pages:	29834
Full texts:	11615
References:	2145

Professor

Doctor of physico-mathematical sciences (1975)

Speciality:

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

Birth date:

23.07.1939

E-mail:

Keywords:

Fourier series, Fourier transforms, Walsh series, Hardy operator, Bellman operator, Hardy–Littlewood operator, dyadic integral, dyadic derivative, approximation by the convolutions, bases of shifts of a function, functions of bounded generalized variation.

Subject:

The Gibbs phenomenon for Riesz spherical means of multiple Fourier series was discovered and the Gibbs constants for these means from below were estimated. The necessary and sufficient conditions for convergence in Pringsheim sense of multiple Fourier series of functions of bounded $\Phi$-variation of Hardy type were obtained. The boundedness of the Hardy operator in real Hardy spaces $H(R)$ and $H(T)$ was proved. The similar result for dyadic Hardy operator was also obtained. The analogue of tauberian theorem of Wiener in dyadic harmonic analysis was proved. As a corollary the following two criteria were obtained: 1) the linear hull of the set $\{f(\cdot\oplus y):y\ge0\}$ of dyadic shifts of a given function $f\in L(\mathbb{R}_+)$ is dens in the space $L(\mathbb{R}_+)$ iff the Walsh–Fourier transform $\tilde f(x)$ is not equal to zero on positive half-line $\mathbb{R}_+$ (dyadic analogue of the criterion of Wiener); 2) in order the linear hull of the set $\{f(\cdot\oplus y):0\le y<1\}$ of all dyadic shifts of the given function $f\in L[0,1)$ be dens in the space $L[0,1)$, it is necessary and sufficient that all Walsh–Fourier coefficients of the function $f\in L[0,1)$ are not equal to zero.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1961 (department of theory of functions and functional analysis). Ph.D. thesis was defended in 1964. D.Sci. thesis was defended in 1975. A list of my works contains more than 80 titles. I am the member of Organizing Committees of Saratov Winter Schools on Function Theory (since 1988), Voronezh Winter Schools on Function Theory (since 1993) and Kazan Summer Schools on Function Theory (since 1995).

Main publications:

B. I. Golubov, A. V. Efimov, V. A. Skvortsov. Ryady i preobrazovaniya Uolsha. Teoriya i primeneniya. M.: Nauka, 1987. (B. Golubov, A. Efimov, V. Skvortsov. Walsh series and transforms. Theory and applications. Kluver Academic Publishers, Dordrecht, Boston, London, 1991).
B. I. Golubov. Elementy dvoichnogo analiza. M.: MGUP, 2005.
B. I. Golubov. Ogranichennost operatorov Khardi i Khardi–Littlvuda v prostranstvakh Re H i BMO // Matem. sb., t. 188, # 7 (1997), 93–106.
B. I. Golubov. Ob analoge neravenstva Khardi dlya preobrazovaniya Fure–Uolsha // Izv. RAN. Ser. matem., t. 65, # 3 (2001), 3–14.
B. I. Golubov. Dvoichnyi analog tauberovoi teoremy Vinera i smezhnye voprosy // Izv. RAN. Ser. matem., t. 67, # 1, (2003), 33–58.
B. I. Golubov. O modifitsirovannom silnom dvoichnom integrale i proizvodnoi // Matem. sb., t. 193, # 4 (2002), 37–60.

https://www.mathnet.ru/eng/person8534

List of publications on Google Scholar

List of publications on ZentralBlatt

https://mathscinet.ams.org/mathscinet/MRAuthorID/220191

https://www.researchgate.net/profile/Boris_Golubov

	Publications in Math-Net.Ru	Citations
	2022
1.	S. S. Volosivets, B. I. Golubov, “Weighted Integrability of Multiple Multiplicative Fourier Transforms”, Mat. Zametki, 111:3 (2022), 365–374 ; Math. Notes, 111:3 (2022), 364–372	1
2.	B. I. Golubov, S. S. Volosivets, “Fourier Transforms of Convolutions of Functions in Lebesgue and Lorentz Spaces”, Trudy Mat. Inst. Steklova, 319 (2022), 94–105 ; Proc. Steklov Inst. Math., 319 (2022), 85–96
	2021
3.	B. I. Golubov, S. S. Volosivets, “Fourier transform and continuity of functions of bounded $\Phi$-variation”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 199 (2021), 43–49
	2019
4.	S. S. Volosivets, B. I. Golubov, “Modified Hardy and Hardy–Littlewood fractional operators in Morrey–Herz spaces and their commutators in weighted spaces”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 171 (2019), 70–77	1
5.	S. S. Volosivets, B. I. Golubov, “Fractional modified Hardy and Hardy–Littlewood operators and their commutators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 9, 16–26 ; Russian Math. (Iz. VUZ), 63:9 (2019), 12–21	1
	2018
6.	S. S. Volosivets, B. I. Golubov, “Generalized absolute convergence of series from Fourier coeficients by systems of Haar type”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 1, 10–20 ; Russian Math. (Iz. VUZ), 62:1 (2018), 7–16	2
	2015
7.	S. S. Volosivets, B. I. Golubov, “Uniform Convergence and Integrability of Multiplicative Fourier Transforms”, Mat. Zametki, 98:1 (2015), 44–60 ; Math. Notes, 98:1 (2015), 53–67	1
	2013
8.	S. S. Volosivets, B. I. Golubov, “Fourier transforms in generalized Lipschitz classes”, Trudy Mat. Inst. Steklova, 280 (2013), 126–137 ; Proc. Steklov Inst. Math., 280 (2013), 120–131	3
	2012
9.	B. I. Golubov, “Absolute convergence of double series of Fourier–Haar coefficients for functions of bounded $p$-variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 6, 3–13 ; Russian Math. (Iz. VUZ), 56:6 (2012), 1–10	9
10.	B. I. Golubov, “Spherical Jump of a Function and the Bochner–Riesz Means of Conjugate Multiple Fourier Series and Fourier Integrals”, Mat. Zametki, 91:4 (2012), 506–514 ; Math. Notes, 91:4 (2012), 479–486	10
	2010
11.	S. S. Volosivets, B. I. Golubov, “Weighted integrability of multiplicative Fourier transforms”, Trudy Mat. Inst. Steklova, 269 (2010), 71–81 ; Proc. Steklov Inst. Math., 269 (2010), 65–75	3
	2008
12.	S. S. Volosivets, B. I. Golubov, “Hardy and Bellman operators in spaces connected with $H(\mathbb T)$ and $BMO(\mathbb T)$”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 5, 4–13 ; Russian Math. (Iz. VUZ), 52:5 (2008), 1–8	1
	2007
13.	B. I. Golubov, “Dyadic distributions”, Mat. Sb., 198:2 (2007), 67–90 ; Sb. Math., 198:2 (2007), 207–230	10
	2006
14.	B. I. Golubov, “Modified Dyadic Integral and Fractional Derivative on $\mathbb R_+$”, Mat. Zametki, 79:2 (2006), 213–233 ; Math. Notes, 79:2 (2006), 196–214	7
	2005
15.	B. I. Golubov, “Fractional Modified Dyadic Integral and Derivative on $\mathbb{R}_+$”, Funktsional. Anal. i Prilozhen., 39:2 (2005), 64–70 ; Funct. Anal. Appl., 39:2 (2005), 64–70	6
	2003
16.	B. I. Golubov, “A dyadic analogue of Wiener's Tauberian theorem and some related questions”, Izv. RAN. Ser. Mat., 67:1 (2003), 33–58 ; Izv. Math., 67:1 (2003), 29–53	7
	2002
17.	B. I. Golubov, “A modified strong dyadic integral and derivative”, Mat. Sb., 193:4 (2002), 37–60 ; Sb. Math., 193:4 (2002), 507–529	19
	2001
18.	B. I. Golubov, “On an analogue of Hardy's inequality for the Walsh–Fourier”, Izv. RAN. Ser. Mat., 65:3 (2001), 3–14 ; Izv. Math., 65:3 (2001), 425–435	12
	1999
19.	B. I. Golubov, “On dyadic analogues of Hardy and Hardy–Littlewood operators”, Sibirsk. Mat. Zh., 40:6 (1999), 1244–1252 ; Siberian Math. J., 40:6 (1999), 1051–1058	5
	1998
20.	B. I. Golubov, “The Hardy and Bellman transforms of the spaces $H^1$ and BMO”, Mat. Zametki, 63:3 (1998), 475–478 ; Math. Notes, 63:3 (1998), 418–421	2
21.	B. I. Golubov, “An analogue of a theorem of Titchmarsh for Walsh-Fourier transformations”, Mat. Sb., 189:5 (1998), 69–86 ; Sb. Math., 189:5 (1998), 707–725	2
	1997
22.	B. I. Golubov, “Boundedness of the Hardy and the Hardy–Littlewood operators in the spaces $\operatorname {Re}H^1$ and $\mathrm {BMO}$”, Mat. Sb., 188:7 (1997), 93–106 ; Sb. Math., 188:7 (1997), 1041–1054	24
	1994
23.	B. I. Golubov, “On a theorem of Bellman on Fourier coefficients”, Mat. Sb., 185:11 (1994), 31–40 ; Russian Acad. Sci. Sb. Math., 83:2 (1995), 321–330	10
	1985
24.	B. I. Golubov, “Absolute convergence of multiple Fourier series”, Mat. Zametki, 37:1 (1985), 13–24 ; Math. Notes, 37:1 (1985), 8–15	8
	1982
25.	B. I. Golubov, “Multiple series and Fourier integrals”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 19 (1982), 3–54 ; J. Soviet Math., 24:6 (1984), 639–673	13
	1981
26.	B. I. Golubov, “Asymptotic behavior of singular multiple integrals for differentiable functions”, Mat. Zametki, 30:5 (1981), 749–762 ; Math. Notes, 30:5 (1981), 873–880	1
27.	B. I. Golubov, “A generalized symmetric derivative and the summability of multiple trigonometric series by the Lebesgue method”, Sibirsk. Mat. Zh., 22:6 (1981), 15–21 ; Siberian Math. J., 22:6 (1981), 815–820
	1980
28.	B. I. Golubov, “On the rate of convergence of integrals of Gauss–Weierstrass type for functions of several variables”, Izv. Akad. Nauk SSSR Ser. Mat., 44:6 (1980), 1255–1278 ; Math. USSR-Izv., 17:3 (1981), 455–475	3
29.	B. I. Golubov, “The Abel-Poisson summation method for multiple Fourier series”, Mat. Zametki, 27:1 (1980), 49–59 ; Math. Notes, 27:1 (1980), 28–33	2
	1979
30.	B. I. Golubov, “On convergence of singular integrals of Gauss–Weierstrass type for functions of several variables”, Dokl. Akad. Nauk SSSR, 248:5 (1979), 1044–1048	1
31.	B. I. Golubov, “On the summability method of Abel–Poisson type for multiple Fourier integrals”, Mat. Sb. (N.S.), 108(150):2 (1979), 229–246 ; Math. USSR-Sb., 36:2 (1980), 213–229	5
	1977
32.	B. I. Golubov, “On the summability of Fourier integrals by Riesz spherical means”, Mat. Sb. (N.S.), 104(146):4(12) (1977), 577–596 ; Math. USSR-Sb., 33:4 (1977), 501–518	2
	1976
33.	B. I. Golubov, “The summability of conjugate multiple Fourier integrals by Riesz means”, Uspekhi Mat. Nauk, 31:5(191) (1976), 237–238	1
	1975
34.	B. I. Golubov, “Approximation of functions of several variables by spherical Riesz means”, Mat. Zametki, 17:2 (1975), 181–191 ; Math. Notes, 17:2 (1975), 108–113
35.	B. I. Golubov, “On convergence of Riesz spherical means of multiple Fourier series”, Mat. Sb. (N.S.), 96(138):2 (1975), 189–211 ; Math. USSR-Sb., 25:2 (1975), 177–197	5
	1974
36.	B. I. Golubov, “Convergence of Riesz spherical means of multiple Fourier series”, Dokl. Akad. Nauk SSSR, 215:1 (1974), 31–34	1
37.	B. I. Golubov, “The approximation of a Hölder class of two variables by Riesz spherical means”, Mat. Zametki, 15:1 (1974), 33–43 ; Math. Notes, 15:1 (1974), 20–25
38.	B. I. Golubov, “The convergence of the double Fourier series of functions of bounded generalized variation. II”, Sibirsk. Mat. Zh., 15:4 (1974), 767–783 ; Siberian Math. J., 15:4 (1974), 546–557	2
39.	B. I. Golubov, “The convergence of the double Fourier series of functions of bounded generalized variation. I”, Sibirsk. Mat. Zh., 15:2 (1974), 262–291 ; Siberian Math. J., 15:2 (1974), 183–204	4
	1973
40.	B. I. Golubov, “The asymptotic $L_p$-norm of differentiated Fourier sums of functions of bounded variation”, Izv. Akad. Nauk SSSR Ser. Mat., 37:2 (1973), 399–421 ; Math. USSR-Izv., 7:2 (1973), 401–423	1
	1972
41.	B. I. Golubov, “Functions of generalized bounded variation, convergence of their Fourier series and conjugate trigonometric series”, Dokl. Akad. Nauk SSSR, 205:6 (1972), 1277–1280	2
42.	B. I. Golubov, “Double Fourier series, and functions of bounded variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 1972, no. 12, 55–68	4
43.	B. I. Golubov, “Determination of the jump of a function of bounded $p$-variation by its Fourier series”, Mat. Zametki, 12:1 (1972), 19–28 ; Math. Notes, 12:1 (1972), 444–449	20
44.	B. I. Golubov, “Asymptotic behavior of the $L_p$-norms of differentiated Fourier sums of functions of bounded variation”, Uspekhi Mat. Nauk, 27:6(168) (1972), 235–236	1
45.	B. I. Golubov, “On the convergence of Riesz spherical means of multiple Fourier series and integrals of functions of bounded generalized variation”, Mat. Sb. (N.S.), 89(131):4(12) (1972), 630–653 ; Math. USSR-Sb., 18:4 (1972), 635–658	13
46.	B. I. Golubov, “Best approximations of functions in the $L_p$ metric by Haar and Walsh polynomials”, Mat. Sb. (N.S.), 87(129):2 (1972), 254–274 ; Math. USSR-Sb., 16:2 (1972), 265–285	16
47.	B. I. Golubov, “Tests of the continuity of functions of bounded $p$-variation”, Sibirsk. Mat. Zh., 13:5 (1972), 1002–1015 ; Siberian Math. J., 13:5 (1972), 693–702	1
	1971
48.	B. I. Golubov, “Series in the Haar system”, Itogi Nauki. Ser. Matematika. Mat. Anal. 1970, 1971, 109–146 ; J. Soviet Math., 1:6 (1973), 704–726	30
49.	B. I. Golubov, “The $p$-variation of functions of two variables”, Izv. Vyssh. Uchebn. Zaved. Mat., 1971, no. 9, 40–49	1
	1969
50.	B. I. Golubov, “The $p$-variation of functions”, Mat. Zametki, 5:2 (1969), 195–204 ; Math. Notes, 5:2 (1969), 119–124	2
	1968
51.	B. I. Golubov, “On functions of bounded $p$-variation”, Izv. Akad. Nauk SSSR Ser. Mat., 32:4 (1968), 837–858 ; Math. USSR-Izv., 2:4 (1968), 799–819	7
52.	B. I. Golubov, “The Fourier integral and the continuity of functions of bounded $p$-variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 1968, no. 11, 83–92	2
53.	B. I. Golubov, “Functions of bounded $p$-variation”, Uspekhi Mat. Nauk, 23:1(139) (1968), 219–220	1
54.	B. I. Golubov, “A certain class of complete orthogonal systems”, Sibirsk. Mat. Zh., 9:2 (1968), 297–314 ; Siberian Math. J., 9:2 (1968), 225–239	19
	1967
55.	B. I. Golubov, “Continuous functions of bounded $p$-variation”, Mat. Zametki, 1:3 (1967), 305–312 ; Math. Notes, 1:3 (1967), 203–207	6
	1966
56.	B. I. Golubov, A. I. Rubinshtein, “A class of convergence systems”, Mat. Sb. (N.S.), 71(113):1 (1966), 96–115	7
	1965
57.	B. I. Golubov, “On absolute convergence of series in Haar's system”, Uspekhi Mat. Nauk, 20:5(125) (1965), 198–202
	1964
58.	B. I. Golubov, “Fourier series of continuous functions relative to a Haar system”, Dokl. Akad. Nauk SSSR, 156:2 (1964), 247–250
59.	B. I. Golubov, “On Fourier series of continuous functions with respect to a Haar system”, Izv. Akad. Nauk SSSR Ser. Mat., 28:6 (1964), 1271–1296	20
60.	B. I. Golubov, “On the summability of sequences”, Izv. Vyssh. Uchebn. Zaved. Mat., 1964, no. 4, 47–55

	2018
61.	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. Math. Mech. Inform., 18:3 (2018), 354–365
	2016
62.	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. Math. Mech. Inform., 16:4 (2016), 485–487
63.	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)”, Uspekhi Mat. Nauk, 71:5(431) (2016), 187–190 ; Russian Math. Surveys, 71:5 (2016), 983–987
64.	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)”, Uspekhi Mat. Nauk, 71:1(427) (2016), 184–186 ; Russian Math. Surveys, 71:1 (2016), 175–177
	2015
65.	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. Math. Mech. Inform., 15:3 (2015), 357–359	1
	2012
66.	B. I. Golubov, B. S. Kashin, L. Yu. Kossovich, S. P. Sidorov, A. P. Khromov, “16 Saratov winter school “Contemporary problems of function theory and its applications””, Izv. Saratov Univ. Math. Mech. Inform., 12:2 (2012), 114–115
	2011
67.	O. V. Besov, S. V. Bochkarev, B. I. Golubov, A. A. Gonchar, M. I. D'yachenko, V. V. Kozlov, S. V. Konyagin, Yu. V. Malykhin, S. M. Nikol'skii, M. K. Potapov, V. A. Sadovnichii, S. A. Telyakovskii, “Boris Sergeevich Kashin (on his 60th birthday)”, Uspekhi Mat. Nauk, 66:4(400) (2011), 189–191 ; Russian Math. Surveys, 66:4 (2011), 825–828
	2008
68.	B. I. Golubov, B. S. Kashin, “Introduction”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 5, 3
69.	B. I. Golubov, A. A. Gonchar, B. S. Kashin, S. M. Nikol'skii, A. M. Olevskii, M. K. Potapov, “On the 80th birthday of Petr Lavrent'evich Ul'yanov”, Uspekhi Mat. Nauk, 63:5(383) (2008), 203–207 ; Russian Math. Surveys, 63:5 (2008), 989–994
	2006
70.	B. I. Golubov, S. M. Nikol'skii, S. A. Telyakovskii, P. L. Ul'yanov, “Károly Tandori (obituary)”, Uspekhi Mat. Nauk, 61:1(367) (2006), 165–168 ; Russian Math. Surveys, 61:1 (2006), 161–164	1
	1982
71.	B. Golubov, “Cohn D. L. Measure theory. Boston etc.: Birkhäuser, 1980, IX+373 p. (Book review)”, Zh. Vychisl. Mat. Mat. Fiz., 22:4 (1982), 1016–1017 ; U.S.S.R. Comput. Math. Math. Phys., 22:4 (1982), 258–259

Presentations in Math-Net.Ru

1.	Приближение полиномами Хаара и Уолша в весовых обобщенных гранд пространствах Лебега S. S. Volosivets, B. I. Golubov XXII International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", dedicated to the 300th anniversary of the Russian Academy of Sciences January 31, 2024 16:50
2.	Some results and problems in dyadic harmonic analysis B. I. Golubov International Conference "Approximation Theory and Applications" Dedicated to the 100th Anniversary S. B. Stechkin September 7, 2021 16:30
3.	Dyadic derivatives and integrals B. Golubov Approximation and discretization September 1, 2021 15:00

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