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Golubov Boris Ivanovich

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Total publications: 57
Scientific articles: 47

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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.

http://www.mathnet.ru/eng/person8534
List of publications on Google Scholar
List of publications on ZentralBlatt
http://www.ams.org/mathscinet/search/author.html?return=viewitems&mrauthid=220191
https://www.researchgate.net/profile/Boris_Golubov

Publications in Math-Net.Ru
1. Generalized absolute convergence of series from Fourier coeficients by systems of Haar type
S. S. Volosivets, B. I. Golubov
Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 1,  10–20
2. Uniform Convergence and Integrability of Multiplicative Fourier Transforms
S. S. Volosivets, B. I. Golubov
Mat. Zametki, 98:1 (2015),  44–60
3. Fourier transforms in generalized Lipschitz classes
S. S. Volosivets, B. I. Golubov
Tr. Mat. Inst. Steklova, 280 (2013),  126–137
4. Absolute convergence of double series of Fourier–Haar coefficients for functions of bounded $p$-variation
B. I. Golubov
Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 6,  3–13
5. Spherical Jump of a Function and the Bochner–Riesz Means of Conjugate Multiple Fourier Series and Fourier Integrals
B. I. Golubov
Mat. Zametki, 91:4 (2012),  506–514
6. Weighted integrability of multiplicative Fourier transforms
S. S. Volosivets, B. I. Golubov
Tr. Mat. Inst. Steklova, 269 (2010),  71–81
7. Hardy and Bellman operators in spaces connected with $H(\mathbb T)$ and $BMO(\mathbb T)$
S. S. Volosivets, B. I. Golubov
Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 5,  4–13
8. Dyadic distributions
B. I. Golubov
Mat. Sb., 198:2 (2007),  67–90
9. Modified Dyadic Integral and Fractional Derivative on $\mathbb R_+$
B. I. Golubov
Mat. Zametki, 79:2 (2006),  213–233
10. Fractional Modified Dyadic Integral and Derivative on $\mathbb{R}_+$
B. I. Golubov
Funktsional. Anal. i Prilozhen., 39:2 (2005),  64–70
11. A dyadic analogue of Wiener's Tauberian theorem and some related questions
B. I. Golubov
Izv. RAN. Ser. Mat., 67:1 (2003),  33–58
12. A modified strong dyadic integral and derivative
B. I. Golubov
Mat. Sb., 193:4 (2002),  37–60
13. On an analogue of Hardy's inequality for the Walsh–Fourier
B. I. Golubov
Izv. RAN. Ser. Mat., 65:3 (2001),  3–14
14. On dyadic analogues of Hardy and Hardy–Littlewood operators
B. I. Golubov
Sibirsk. Mat. Zh., 40:6 (1999),  1244–1252
15. The Hardy and Bellman transforms of the spaces $H^1$ and BMO
B. I. Golubov
Mat. Zametki, 63:3 (1998),  475–478
16. An analogue of a theorem of Titchmarsh for Walsh-Fourier transformations
B. I. Golubov
Mat. Sb., 189:5 (1998),  69–86
17. Boundedness of the Hardy and the Hardy–Littlewood operators in the spaces $\operatorname {Re}H^1$ and $\mathrm {BMO}$
B. I. Golubov
Mat. Sb., 188:7 (1997),  93–106
18. On a theorem of Bellman on Fourier coefficients
B. I. Golubov
Mat. Sb., 185:11 (1994),  31–40
19. Absolute convergence of multiple Fourier series
B. I. Golubov
Mat. Zametki, 37:1 (1985),  13–24
20. Multiple series and Fourier integrals
B. I. Golubov
Itogi Nauki i Tekhn. Ser. Mat. Anal., 19 (1982),  3–54
21. Asymptotic behavior of singular multiple integrals for differentiable functions
B. I. Golubov
Mat. Zametki, 30:5 (1981),  749–762
22. On the rate of convergence of integrals of Gauss–Weierstrass type for functions of several variables
B. I. Golubov
Izv. Akad. Nauk SSSR Ser. Mat., 44:6 (1980),  1255–1278
23. The Abel-Poisson summation method for multiple Fourier series
B. I. Golubov
Mat. Zametki, 27:1 (1980),  49–59
24. On the summability method of Abel–Poisson type for multiple Fourier integrals
B. I. Golubov
Mat. Sb. (N.S.), 108(150):2 (1979),  229–246
25. On the summability of Fourier integrals by Riesz spherical means
B. I. Golubov
Mat. Sb. (N.S.), 104(146):4(12) (1977),  577–596
26. The summability of conjugate multiple Fourier integrals by Riesz means
B. I. Golubov
Uspekhi Mat. Nauk, 31:5(191) (1976),  237–238
27. Approximation of functions of several variables by spherical Riesz means
B. I. Golubov
Mat. Zametki, 17:2 (1975),  181–191
28. On convergence of Riesz spherical means of multiple Fourier series
B. I. Golubov
Mat. Sb. (N.S.), 96(138):2 (1975),  189–211
29. The approximation of a Hölder class of two variables by Riesz spherical means
B. I. Golubov
Mat. Zametki, 15:1 (1974),  33–43
30. The asymptotic $L_p$-norm of differentiated Fourier sums of functions of bounded variation
B. I. Golubov
Izv. Akad. Nauk SSSR Ser. Mat., 37:2 (1973),  399–421
31. Double Fourier series, and functions of bounded variation
B. I. Golubov
Izv. Vyssh. Uchebn. Zaved. Mat., 1972, no. 12,  55–68
32. Determination of the jump of a function of bounded $p$-variation by its Fourier series
B. I. Golubov
Mat. Zametki, 12:1 (1972),  19–28
33. Asymptotic behavior of the $L_p$-norms of differentiated Fourier sums of functions of bounded variation
B. I. Golubov
Uspekhi Mat. Nauk, 27:6(168) (1972),  235–236
34. On the convergence of Riesz spherical means of multiple Fourier series and integrals of functions of bounded generalized variation
B. I. Golubov
Mat. Sb. (N.S.), 89(131):4(12) (1972),  630–653
35. Best approximations of functions in the $L_p$ metric by Haar and Walsh polynomials
B. I. Golubov
Mat. Sb. (N.S.), 87(129):2 (1972),  254–274
36. Series in the Haar system
B. I. Golubov
Itogi Nauki. Ser. Matematika. Mat. Anal. 1970, 1971,  109–146
37. The $p$-variation of functions of two variables
B. I. Golubov
Izv. Vyssh. Uchebn. Zaved. Mat., 1971, no. 9,  40–49
38. The $p$-variation of functions
B. I. Golubov
Mat. Zametki, 5:2 (1969),  195–204
39. On functions of bounded $p$-variation
B. I. Golubov
Izv. Akad. Nauk SSSR Ser. Mat., 32:4 (1968),  837–858
40. The Fourier integral and the continuity of functions of bounded $p$-variation
B. I. Golubov
Izv. Vyssh. Uchebn. Zaved. Mat., 1968, no. 11,  83–92
41. Functions of bounded $p$-variation
B. I. Golubov
Uspekhi Mat. Nauk, 23:1(139) (1968),  219–220
42. Continuous functions of bounded $p$-variation
B. I. Golubov
Mat. Zametki, 1:3 (1967),  305–312
43. A class of convergence systems
B. I. Golubov, A. I. Rubinshtein
Mat. Sb. (N.S.), 71(113):1 (1966),  96–115
44. On absolute convergence of series in Haar's system
B. I. Golubov
Uspekhi Mat. Nauk, 20:5(125) (1965),  198–202
45. Fourier series of continuous functions relative to a Haar system
B. I. Golubov
Dokl. Akad. Nauk SSSR, 156:2 (1964),  247–250
46. On Fourier series of continuous functions with respect to a Haar system
B. I. Golubov
Izv. Akad. Nauk SSSR Ser. Mat., 28:6 (1964),  1271–1296
47. On the summability of sequences
B. I. Golubov
Izv. Vyssh. Uchebn. Zaved. Mat., 1964, no. 4,  47–55

48. 18th International Saratov Winter School “Contemporary Problems of Function Theory and Their Applications”
B. I. Golubov, B. S. Kashin, L. Yu. Kossovich, S. P. Sidorov, A. P. Khromov, A. N. Chumachenko
Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 16:4 (2016),  485–487
49. Evgenii Sergeevich Polovinkin (on his 70th birthday)
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
Uspekhi Mat. Nauk, 71:5(431) (2016),  187–190
50. Valentin Anatol'evich Skvortsov (on his 80th birthday)
B. I. Golubov, B. S. Kashin, T. P. Lukashenko, M. G. Plotnikov, M. A. Skopina, A. P. Solodov, A. M. Stepin, N. N. Kholshchevnikova
Uspekhi Mat. Nauk, 71:1(427) (2016),  184–186
51. XVII International Saratov Winter School «Contemporary Problems of the Function Theory and its Applications». Dedicated to the 150th Anniversary of V.  A. Steklov
B. I. Golubov, B. S. Kashin, L. Yu. Kossovich, S. P. Sidorov, A. P. Khromov
Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 15:3 (2015),  357–359
52. 16 Saratov winter school “Contemporary problems of function theory and its applications”
B. I. Golubov, B. S. Kashin, L. Yu. Kossovich, S. P. Sidorov, A. P. Khromov
Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 12:2 (2012),  114–115
53. Boris Sergeevich Kashin (on his 60th birthday)
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
Uspekhi Mat. Nauk, 66:4(400) (2011),  189–191
54. Introduction
B. I. Golubov, B. S. Kashin
Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 5,  3
55. On the 80th birthday of Petr Lavrent'evich Ul'yanov
B. I. Golubov, A. A. Gonchar, B. S. Kashin, S. M. Nikol'skii, A. M. Olevskii, M. K. Potapov
Uspekhi Mat. Nauk, 63:5(383) (2008),  203–207
56. Károly Tandori (obituary)
B. I. Golubov, S. M. Nikol'skii, S. A. Telyakovskii, P. L. Ul'yanov
Uspekhi Mat. Nauk, 61:1(367) (2006),  165–168
57. Cohn D. L. Measure theory. Boston etc.: Birkhäuser, 1980, IX+373 p. (Book review)
B. Golubov
Zh. Vychisl. Mat. Mat. Fiz., 22:4 (1982),  1016–1017

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