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Golubov, Boris Ivanovich

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Total publications: 68
Scientific articles: 57

Number of views:
This page:4063
Abstract pages:20642
Full texts:7391
References:1356
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
https://mathscinet.ams.org/mathscinet/MRAuthorID/220191
https://www.researchgate.net/profile/Boris_Golubov

Publications in Math-Net.Ru
2019
1. 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. Ser. Sovrem. Mat. Pril. Temat. Obz., 171 (2019),  70–77  mathnet
2. S. S. Volosivets, B. I. Golubov, “Fractional modified Hardy and Hardy–Littlewood operators and their commutators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, 9,  16–26  mathnet
2018
3. 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, 1,  10–20  mathnet; Russian Math. (Iz. VUZ), 62:1 (2018), 7–16  isi  scopus
2015
4. S. S. Volosivets, B. I. Golubov, “Uniform Convergence and Integrability of Multiplicative Fourier Transforms”, Mat. Zametki, 98:1 (2015),  44–60  mathnet  mathscinet  elib; Math. Notes, 98:1 (2015), 53–67  isi  scopus
2013
5. S. S. Volosivets, B. I. Golubov, “Fourier transforms in generalized Lipschitz classes”, Tr. Mat. Inst. Steklova, 280 (2013),  126–137  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 280 (2013), 120–131  isi  elib  scopus
2012
6. B. I. Golubov, “Absolute convergence of double series of Fourier–Haar coefficients for functions of bounded $p$-variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, 6,  3–13  mathnet  mathscinet; Russian Math. (Iz. VUZ), 56:6 (2012), 1–10  scopus
7. 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  mathnet  mathscinet  elib; Math. Notes, 91:4 (2012), 479–486  isi  elib  scopus
2010
8. S. S. Volosivets, B. I. Golubov, “Weighted integrability of multiplicative Fourier transforms”, Tr. Mat. Inst. Steklova, 269 (2010),  71–81  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 269 (2010), 65–75  isi  elib  scopus
2008
9. 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, 5,  4–13  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 52:5 (2008), 1–8
2007
10. B. I. Golubov, “Dyadic distributions”, Mat. Sb., 198:2 (2007),  67–90  mathnet  mathscinet  zmath  elib; Sb. Math., 198:2 (2007), 207–230  isi  scopus
2006
11. B. I. Golubov, “Modified Dyadic Integral and Fractional Derivative on $\mathbb R_+$”, Mat. Zametki, 79:2 (2006),  213–233  mathnet  mathscinet  zmath  elib; Math. Notes, 79:2 (2006), 196–214  isi  scopus
2005
12. B. I. Golubov, “Fractional Modified Dyadic Integral and Derivative on $\mathbb{R}_+$”, Funktsional. Anal. i Prilozhen., 39:2 (2005),  64–70  mathnet  mathscinet  zmath; Funct. Anal. Appl., 39:2 (2005), 64–70  scopus
2003
13. B. I. Golubov, “A dyadic analogue of Wiener's Tauberian theorem and some related questions”, Izv. RAN. Ser. Mat., 67:1 (2003),  33–58  mathnet  mathscinet  zmath; Izv. Math., 67:1 (2003), 29–53  isi  scopus
2002
14. B. I. Golubov, “A modified strong dyadic integral and derivative”, Mat. Sb., 193:4 (2002),  37–60  mathnet  mathscinet  zmath  elib; Sb. Math., 193:4 (2002), 507–529  isi  scopus
2001
15. B. I. Golubov, “On an analogue of Hardy's inequality for the Walsh–Fourier”, Izv. RAN. Ser. Mat., 65:3 (2001),  3–14  mathnet  mathscinet  zmath; Izv. Math., 65:3 (2001), 425–435  scopus
1999
16. B. I. Golubov, “On dyadic analogues of Hardy and Hardy–Littlewood operators”, Sibirsk. Mat. Zh., 40:6 (1999),  1244–1252  mathnet  mathscinet  zmath; Siberian Math. J., 40:6 (1999), 1051–1058  isi
1998
17. B. I. Golubov, “The Hardy and Bellman transforms of the spaces $H^1$ and BMO”, Mat. Zametki, 63:3 (1998),  475–478  mathnet  mathscinet  zmath; Math. Notes, 63:3 (1998), 418–421  isi
18. B. I. Golubov, “An analogue of a theorem of Titchmarsh for Walsh-Fourier transformations”, Mat. Sb., 189:5 (1998),  69–86  mathnet  mathscinet  zmath; Sb. Math., 189:5 (1998), 707–725  isi  scopus
1997
19. 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  mathnet  mathscinet  zmath; Sb. Math., 188:7 (1997), 1041–1054  isi  scopus
1994
20. B. I. Golubov, “On a theorem of Bellman on Fourier coefficients”, Mat. Sb., 185:11 (1994),  31–40  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 83:2 (1995), 321–330  isi
1985
21. B. I. Golubov, “Absolute convergence of multiple Fourier series”, Mat. Zametki, 37:1 (1985),  13–24  mathnet  mathscinet  zmath; Math. Notes, 37:1 (1985), 8–15  isi
1982
22. B. I. Golubov, “Multiple series and Fourier integrals”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 19 (1982),  3–54  mathnet  mathscinet  zmath; J. Soviet Math., 24:6 (1984), 639–673
1981
23. B. I. Golubov, “Asymptotic behavior of singular multiple integrals for differentiable functions”, Mat. Zametki, 30:5 (1981),  749–762  mathnet  mathscinet  zmath; Math. Notes, 30:5 (1981), 873–880
24. 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  mathnet  mathscinet  zmath; Siberian Math. J., 22:6 (1981), 815–820  isi
1980
25. 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  mathnet  mathscinet  zmath; Math. USSR-Izv., 17:3 (1981), 455–475  isi
26. B. I. Golubov, “The Abel-Poisson summation method for multiple Fourier series”, Mat. Zametki, 27:1 (1980),  49–59  mathnet  mathscinet  zmath; Math. Notes, 27:1 (1980), 28–33  isi
1979
27. 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  mathnet  mathscinet  zmath
28. 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  mathnet  mathscinet  zmath; Math. USSR-Sb., 36:2 (1980), 213–229  isi
1977
29. B. I. Golubov, “On the summability of Fourier integrals by Riesz spherical means”, Mat. Sb. (N.S.), 104(146):4(12) (1977),  577–596  mathnet  mathscinet  zmath; Math. USSR-Sb., 33:4 (1977), 501–518  isi
1976
30. B. I. Golubov, “The summability of conjugate multiple Fourier integrals by Riesz means”, Uspekhi Mat. Nauk, 31:5(191) (1976),  237–238  mathnet  mathscinet  zmath
1975
31. B. I. Golubov, “Approximation of functions of several variables by spherical Riesz means”, Mat. Zametki, 17:2 (1975),  181–191  mathnet  mathscinet  zmath; Math. Notes, 17:2 (1975), 108–113
32. B. I. Golubov, “On convergence of Riesz spherical means of multiple Fourier series”, Mat. Sb. (N.S.), 96(138):2 (1975),  189–211  mathnet  mathscinet  zmath; Math. USSR-Sb., 25:2 (1975), 177–197
1974
33. B. I. Golubov, “Convergence of Riesz spherical means of multiple Fourier series”, Dokl. Akad. Nauk SSSR, 215:1 (1974),  31–34  mathnet  mathscinet  zmath
34. B. I. Golubov, “The approximation of a Hölder class of two variables by Riesz spherical means”, Mat. Zametki, 15:1 (1974),  33–43  mathnet  mathscinet  zmath; Math. Notes, 15:1 (1974), 20–25
35. 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  mathnet  mathscinet  zmath; Siberian Math. J., 15:4 (1974), 546–557  isi
36. 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  mathnet  mathscinet  zmath; Siberian Math. J., 15:2 (1974), 183–204
1973
37. 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  mathnet  mathscinet  zmath; Math. USSR-Izv., 7:2 (1973), 401–423
1972
38. 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  mathnet  mathscinet  zmath
39. B. I. Golubov, “Double Fourier series, and functions of bounded variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 1972, 12,  55–68  mathnet  mathscinet  zmath
40. 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  mathnet  mathscinet  zmath; Math. Notes, 12:1 (1972), 444–449
41. 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  mathnet  mathscinet  zmath
42. 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  mathnet  mathscinet  zmath; Math. USSR-Sb., 18:4 (1972), 635–658
43. 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  mathnet  mathscinet  zmath; Math. USSR-Sb., 16:2 (1972), 265–285
44. B. I. Golubov, “Tests of the continuity of functions of bounded $p$-variation”, Sibirsk. Mat. Zh., 13:5 (1972),  1002–1015  mathnet  mathscinet  zmath; Siberian Math. J., 13:5 (1972), 693–702
1971
45. B. I. Golubov, “Series in the Haar system”, Itogi Nauki. Ser. Matematika. Mat. Anal. 1970, 1971,  109–146  mathnet  mathscinet  zmath; J. Soviet Math., 1:6 (1973), 704–726
46. B. I. Golubov, “The $p$-variation of functions of two variables”, Izv. Vyssh. Uchebn. Zaved. Mat., 1971, 9,  40–49  mathnet  mathscinet  zmath
1969
47. B. I. Golubov, “The $p$-variation of functions”, Mat. Zametki, 5:2 (1969),  195–204  mathnet  mathscinet  zmath; Math. Notes, 5:2 (1969), 119–124
1968
48. B. I. Golubov, “On functions of bounded $p$-variation”, Izv. Akad. Nauk SSSR Ser. Mat., 32:4 (1968),  837–858  mathnet  mathscinet  zmath; Math. USSR-Izv., 2:4 (1968), 799–819
49. B. I. Golubov, “The Fourier integral and the continuity of functions of bounded $p$-variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 1968, 11,  83–92  mathnet  mathscinet  zmath
50. B. I. Golubov, “Functions of bounded $p$-variation”, Uspekhi Mat. Nauk, 23:1(139) (1968),  219–220  mathnet  mathscinet  zmath
51. B. I. Golubov, “A certain class of complete orthogonal systems”, Sibirsk. Mat. Zh., 9:2 (1968),  297–314  mathnet  mathscinet  zmath; Siberian Math. J., 9:2 (1968), 225–239
1967
52. B. I. Golubov, “Continuous functions of bounded $p$-variation”, Mat. Zametki, 1:3 (1967),  305–312  mathnet  mathscinet  zmath; Math. Notes, 1:3 (1967), 203–207
1966
53. B. I. Golubov, A. I. Rubinshtein, “A class of convergence systems”, Mat. Sb. (N.S.), 71(113):1 (1966),  96–115  mathnet  mathscinet  zmath
1965
54. B. I. Golubov, “On absolute convergence of series in Haar's system”, Uspekhi Mat. Nauk, 20:5(125) (1965),  198–202  mathnet  mathscinet  zmath
1964
55. B. I. Golubov, “Fourier series of continuous functions relative to a Haar system”, Dokl. Akad. Nauk SSSR, 156:2 (1964),  247–250  mathnet  mathscinet  zmath
56. 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  mathnet  mathscinet  zmath
57. B. I. Golubov, “On the summability of sequences”, Izv. Vyssh. Uchebn. Zaved. Mat., 1964, 4,  47–55  mathnet  mathscinet  zmath

2018
58. 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
2016
59. 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
60. 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  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 71:5 (2016), 983–987  isi
61. 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  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 71:1 (2016), 175–177  isi
2015
62. 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
2012
63. 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. (N.S.), Ser. Math. Mech. Inform., 12:2 (2012),  114–115  mathnet
2011
64. 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  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 66:4 (2011), 825–828  isi
2008
65. B. I. Golubov, B. S. Kashin, “Introduction”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, 5,  3  mathnet
66. 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  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:5 (2008), 989–994  isi
2006
67. 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  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 61:1 (2006), 161–164  isi
1982
68. 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  mathnet; U.S.S.R. Comput. Math. Math. Phys., 22:4 (1982), 258–259

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