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Bochkarev Sergei Viktorovich

Total publications: 73 (70)
in MathSciNet: 67 (64)
in zbMATH: 60 (58)
in Web of Science: 13 (10)
in Scopus: 23 (23)
Cited articles: 46
Citations in Math-Net.Ru: 162
Citations in MathSciNet (by Sep 2017): 141
Citations in Web of Science: 15
Citations in Scopus: 42
Presentations: 5

Number of views:
This page:4036
Abstract pages:10370
Full texts:2835
References:706
Doctor of physico-mathematical sciences (1974)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Phone: +7 (495) 984 81 41 * 37 89
E-mail:
Keywords: convergence and unconditional convergence almost everywhere, Walsh system, absolute convergence, classical and general orthogonal systems, multiplicative inequalities, exponential sums.
UDC: 517.522.3, 517.512.2/.4, 513.881, 517.53, 517.5, 517.522, 577.5

Subject:

Trigonometic and orthogonal series, functional spaces, bases, almost everywhere convergence, exponential sums, BMO and Hardy spaces, multiplicative systems.

   
Main publications:
  1. S. V. Bochkarev, “A Generalization of Kolmogorov's Theorem to Biorthogonal Systems”, Proc. Steklov Inst. Math., 260 (2008), 37–49  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
  2. S. V. Bochkarev, “Multiplicative Inequalities for the $L_1$ Norm: Applications in Analysis and Number Theory”, Proc. Steklov Inst. Math., 255 (2006), 49–64  mathnet  crossref  mathscinet  elib  scopus
  3. S. V. Bochkarev, “Everywhere divergent Fourier series with respect to the Walsh system and with respect to multiplicative systems”, Russian Math. Surveys, 59:1 (2004), 103–124  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  4. S. V. Bochkarev, “The method of averaging in the theory of orthogonal series and some questions in the theory of bases”, Proc. Steklov Inst. Math., 146 (1980), 1–92  mathnet  mathscinet  mathscinet  zmath
  5. S. V. Bochkarev, “Existence of a basis in the space of functions analytic in the disk, and some properties of Franklin's system”, Math. USSR-Sb., 24:1 (1974), 1–16  mathnet  crossref  mathscinet  zmath  scopus

http://www.mathnet.ru/eng/person14011
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:bochkarev.sergei-viktorovich
https://mathscinet.ams.org/mathscinet/MRAuthorID/206796
http://elibrary.ru/author_items.asp?authorid=4663
http://www.researcherid.com/rid/Q-4531-2016
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Full list of publications:
| by years | by types | by times cited | scientific publications | common list |


1. S. V. Bochkarev, “Abstract Kolmogorov theorem, applications to metric spaces and topological groups”, Mat. Sb. (to appear)  mathnet

   2015
2. S. V. Bochkarev, “Kolmogorov’s abstract theorem: Application to metric spaces and topological groups”, Dokl. Math., 91:3 (2015), 367–370  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus

   2014
3. S. V. Bochkarev, “de la Vallée-Poussin means of Fourier series for the quadratic spectrum and for spectra with power-like density”, Russian Math. Surveys, 69:1 (2014), 119–152  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus

   2013
4. O. V. Besov, S. V. Bochkarev, E. A. Volkov, V. A. Il'in, B. S. Kashin, V. V. Kozlov, S. V. Konyagin, N. N. Kudryavtsev, Yu. S. Osipov, S. I. Pokhozhaev, V. A. Sadovnichii, A. G. Sergeev, S. A. Telyakovskii, “His mathematical century (to the memory of Sergei Mikhailovich Nikol'skii)”, Russian Math. Surveys, 68:3 (2013), 591–594  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib

   2012
5. S. V. Bochkarev, “Srednie Valle Pussena ryadov Fure dlya kvadratichnogo spektra i spektrov stepennoi plotnosti”, VII Mezhdunarodnyi simpozium «Ryady Fure i ikh prilozheniya» (Rostov-na-Donu, 2012 g.), Tezisy dokladov, Yuzhnyi federalnyi universitet, 2012, 12–13

   2011
6. Bochkarev S.V., “De la Vallee-Poussin Means of Fourier Series for Quadratic Spectrum and Power Density Spectra”, Dokl. Math., 84:1 (2011), 485–490  crossref  mathscinet (cited: 1)  zmath  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
7. 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)”, Russian Math. Surveys, 66:4 (2011), 825–828  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib

   2010
8. S. V. Bochkarev, “On a problem of Hardy for Walsh-Fourier series”, Dokl. Math., 81:3 (2010), 390–391  crossref  mathscinet  zmath  isi  elib  elib  scopus

   2008
9. S. V. Bochkarev, “Multiplikativnye neravenstva dlya klassov Khardi, primenennye k eksponentsialnym summam po prostym chislam”, Simpozium «Ryady Fure i ikh prilozheniya», Rostov-na-Donu, 2008, 14
10. S. V. Bochkarev, “A Generalization of Kolmogorov's Theorem to Biorthogonal Systems”, Proc. Steklov Inst. Math., 260 (2008), 37–49  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 2)

   2009
11. S. V. Bochkarev, “Multiplicative Bounds for $L_1$-Norms of Exponential Sums”, Journal of Mathematical Sciences, 155:1 (2009), 47–56  mathnet  crossref  mathscinet  scopus

   2007
12. S. V. Bochkarev, “Obobschenie teoremy Kolmogorova na biortogonalnye sistemy”, Teoriya funktsii i vychislitelnye metody, Materialy mezhdunarodnoi konferentsii (Astana, 2007), Astana, 2007, 70–72

   2006
13. S. V. Bochkarev, “Multiplicative Inequalities for the $L_1$ Norm: Applications in Analysis and Number Theory”, Proc. Steklov Inst. Math., 255 (2006), 49–64  mathnet  crossref  mathscinet  elib (cited: 5)  scopus (cited: 2)

   2005
14. S. V. Bochkarev, “New multiplicative inequalities and estimates for the $L_1$-norms of trigonometric series and polynomials”, Dokl. Math., 72:2 (2005), 762–765  mathnet  mathscinet  zmath  isi (cited: 2)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 2)
15. S. V. Bochkarev, “New Inequalities in the Littlewood–Paley Theory and Estimates of the $L_1$ Norm of Trigonometric Series and Polynomials”, Proc. Steklov Inst. Math., 248 (2005), 59–68  mathnet  mathscinet  zmath

   2004
16. S. V. Bochkarev, “Everywhere divergent Fourier series with respect to the Walsh system and with respect to multiplicative systems”, Russian Math. Surveys, 59:1 (2004), 103–124  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 8)  elib (cited: 12)  scopus (cited: 9)

   2003
17. S. V. Bochkarev, “Everywhere divergent Fourier-Walsh series”, Dokl. Math., 67:3 (2003), 307–310  mathnet  mathscinet  zmath  isi (cited: 1)  elib (cited: 1)  scopus (cited: 1)
18. S. V. Bochkarev, “Multiplicative Inequalities for Functions from the Hardy Space $H^1$ and Their Application to the Estimation of Exponential Sums”, Proc. Steklov Inst. Math., 243 (2003), 89–97  mathnet  mathscinet  zmath

   2002
19. S. V. Bochkarev, “A new method for estimating the integral norm of exponential sums: application to quadratic sums”, Dokl. Math., 66:2 (2002), 210–212  mathnet  mathscinet  zmath  zmath  isi (cited: 2)  elib (cited: 2)  scopus (cited: 2)

   2001
20. S. V. Bochkarev, “A Method for Estimating the $L_1$ Norm of an Exponential Sum Based on Arithmetic Properties of the Spectrum”, Proc. Steklov Inst. Math., 232 (2001), 88–95  mathnet  mathscinet  zmath

   2000
21. S. V. Bochkarev, “On the problem of the smoothness of functions whose Fourier-Walsh series diverge almost everywhere”, Dokl. Math., 61:2 (2000), 263–266  mathnet  mathscinet  zmath  elib (cited: 2)  scopus (cited: 2)
22. S. V. Bochkarev, “Inequalities for orthogonal series and a strengthening of the theorems of Carleman and Orlicz”, Dokl. Math., 61:2 (2000), 165–168  mathnet  mathscinet  zmath  elib (cited: 1)  scopus (cited: 1)

   1999
23. S. V. Bochkarev, “Multiplikativnye otsenki $L_1$-normy eksponentsialnykh summ”, Metricheskaya teoriya funktsii i smezhnye voprosy analiza, Izd-vo AFTs, M., 1999, 57–68  mathscinet (cited: 1)

   1998
24. S. V. Bochkarev, “Estimation of the Fourier coefficients of functions from Lorentz spaces”, Dokl. Math., 57:3 (1998), 454–457  mathnet  mathscinet  zmath  elib (cited: 2)  scopus (cited: 2)

   1997
25. S. V. Bochkarev, “Hausdorff–Young–Riesz Theorem in Lorentz Spaces and Multiplicative Inequalities”, Proc. Steklov Inst. Math., 219 (1997), 96–107  mathnet  mathscinet  zmath
26. S. V. Bochkarev, “On a method for estimating the $L_1$-norm of an exponential sum”, Proc. Steklov Inst. Math., 218 (1997), 69–71  mathnet  mathscinet  zmath

   1995
27. S. V. Bochkarev, “Vallé-Poussin series in the spaces BMO, $L_1$, and $H^1(D)$ and multiplier inequalities”, Proc. Steklov Inst. Math., 210 (1995), 30–46  mathnet  mathscinet  zmath
28. S. V. Bochkarev, “The de la Vallée-Poussin series in the spaces BMO, $L_1$ and $H^1(D)$, and multiplicative inequalities”, Dokl. Math., 52:2 (1995), 260–263  mathnet  mathscinet  zmath
29. O. V. Besov, S. V. Bochkarev, V. S. Vladimirov, E. A. Volkov, V. K. Dzyadyk, V. A. Il'in, B. S. Kashin, N. P. Korneichuk, L. D. Kudryavtsev, O. A. Oleinik, Yu. S. Osipov, S. I. Pokhozhaev, S. B. Stechkin, S. A. Telyakovskii, V. N. Temlyakov, P. L. Ul'yanov, “Sergei Mikhailovich Nikol'skii (on his ninetieth birthday)”, Russian Math. Surveys, 50:6 (1995), 1321–1327  mathnet  crossref  mathscinet  adsnasa  isi

   1994
30. S. V. Bochkarev, “Convergence almost everywhere of Dini-type integrals”, Russian Acad. Sci. Dokl. Math., 49:1 (1994), 183–188  mathnet  mathscinet  zmath
31. S. V. Bochkarev, “Series generated by Steklov functions”, Russian Acad. Sci. Dokl. Math., 49:1 (1994), 154–159  mathnet  mathscinet  zmath

   1995
32. S. V. Bochkarev, “Estimates of some character sums”, Proc. Steklov Inst. Math., 207 (1995), 41–50  mathnet  mathscinet  zmath

   1994
33. S. V. Bochkarev, “Almost everywhere divergent rearragements of Fourier series of the class $H^\omega$ with respect to multiplicative systems of functions”, Proc. Steklov Inst. Math., 201 (1994), 95–107  mathnet  mathscinet  zmath

   1991
34. S. V. Bochkarev, “Rearrangements of multiplicative systems”, Soviet Math. Dokl., 43:3 (1991), 708–710 (1992)  mathnet  mathscinet  zmath

   1990
35. S. V. Bochkarev, “Rearrangements of periodic multiplicative orthogonal series”, Colloq. Math., 60/61:1 (1990), 291–299  mathscinet (cited: 1)  zmath

   1992
36. S. V. Bochkarev, “Bases in functional spaces and the Franklin system”, Proc. Steklov Inst. Math., 190 (1992), 19–37  mathnet  mathscinet  zmath

   1987
37. S. V. Bochkariev, “Probabilistic method of approach to the certain problems of Fourier analysis”, Proceedings of the 1st World Congress of the Bernoulli Society (Tashkent, 1986), v. 1, VNU Sci. Press, Utrecht, 1987, 567–570  mathscinet

   1989
38. S. V. Bochkarev, “The conjugate Franklin system is a basis in the space of continuous functions”, Proc. Steklov Inst. Math., 180 (1989), 66–67  mathnet  zmath

   1985
39. S. V. Bochkarev, “The conjugate Franklin system is a basis in the space of continuous functions”, Soviet Math. Dokl., 32 (1985), 701–705  mathnet  mathscinet  zmath

   1987
40. S. V. Bochkarev, “Construction of a dyadic interpolation basis in the space of continuous functions using Fejér kernels”, Proc. Steklov Inst. Math., 172 (1987), 29–66  mathnet  mathscinet  zmath

   1985
41. S. V. Bochkarev, “Construction of a dyadic interpolation basis in the space of continuous functions on the basis of Fejér kernels”, Soviet Math. Dokl., 31 (1985), 475–476  mathnet  mathscinet  zmath

   1984
42. S. V. Bochkarev, “Postroenie polinomialnykh bazisov v konechnomernykh prostranstvakh analiticheskikh funktsii.”, Trudy mezhdunarodnoi konferentsii po teorii priblizheniya funktsii, Nauk. dumka, Kiev, 1984, 66–69

   1985
43. S. V. Bochkarev, “Construction of polynomial bases in finite-dimensional spaces of functions analytic in the disk”, Proc. Steklov Inst. Math., 164 (1985), 55–81  mathnet  mathscinet  zmath

   1982
44. S. V. Bochkarev, “Construction of basis in finite-dimensional spaces of analytic functions in the disk”, Soviet Math. Dokl., 25 (1982), 859–860  mathscinet  zmath
45. S. V. Bochkarev, “Construction of polynomial bases in finite-dimensional spaces of functions analytic in the disk”, Recent trends in Mathematics, Teubner-Texts. Band 50. Leipzig, 1982, 38–46

   1981
46. S. V. Bochkarev, “The averaging Method in the theory of orthogonal series”, Eight lectures delivered at the ICM, Helsinki, AMS Trans. ser. 2, 117 (1981), 23–29  mathscinet (cited: 1)

   1980
47. S. V. Bochkarev, “Rearrangements of Fourier–Walsh series”, Math. USSR-Izv., 15:2 (1980), 259–275  mathnet  crossref  mathscinet  zmath  adsnasa  isi

   1978
48. S. V. Bockarev, “On a majorant of the partial sums for a rearranged Walsh system”, Soviet Math. Dokl., 19 (1978), 341–342  mathscinet  zmath

   1980
49. S. V. Bochkarev, “The method of averaging in the theory of orthogonal series and some questions in the theory of bases”, Proc. Steklov Inst. Math., 146 (1980), 1–92  mathnet  mathscinet (cited: 4)  mathscinet (cited: 4)  zmath

   1976
50. S. V. Bochkarev, “Classes of functions and Fourier coefficients with respect to complete orthonormal systems”, Math. Notes, 20:3 (1976), 805–816  mathnet  crossref  mathscinet  zmath  scopus

   1975
51. S. V. Bockarev, “A Fourier series in an arbitrary bounded orthonormal system that diverges on a set of positive measure”, Soviet Math. Dokl., 16 (1975), 1441–1442 (1976)  mathscinet  zmath
52. S. V. Bočkarev, “Some inequalities for Franklin series”, Anal. Math., 1:4 (1975), 249–257  crossref  mathscinet (cited: 7)  elib  scopus (cited: 12)
53. S. V. Bockarev, “Logarithmic growth of arithmetic means of Lebesgue functions of bounded orthonormal systems”, Soviet Math. Dokl., 16 (1975), 799–802  mathscinet  zmath
54. S. V. Bochkarev, “A Fourier series in an arbitrary bounded orthonormal system that diverges on a set of positive measure”, Math. USSR-Sb., 27:3 (1975), 393–405  mathnet  crossref  mathscinet  zmath

   1974
55. S. V. Bockarev, “On a basis in the space of functions continuous in the closed disc and analytic inside it”, Soviet Math. Dokl., 15 (1974), 1195–1198  mathscinet  zmath  scopus
56. S. V. Bochkarev, “Absolute convergence of Fourier series with respect to bounded systems”, Math. Notes, 15:3 (1974), 207–211  mathnet  crossref  mathscinet  zmath  elib (cited: 2)  scopus (cited: 2)
57. S. V. Bochkarev, “Existence of a basis in the space of functions analytic in the disk, and some properties of Franklin's system”, Math. USSR-Sb., 24:1 (1974), 1–16  mathnet  crossref  mathscinet  zmath  scopus (cited: 2)
58. S. V. Bochkarev, “On the absolute convergence of Fourier series in bounded complete orthonormal systems of functions”, Math. USSR-Sb., 22:1 (1974), 201–216  mathnet  crossref  mathscinet  zmath
59. S. V. Bochkarev, Klassy funktsii i koeffitsienty Fure po polnym ortonormirovannym sistemam, Diss. … dokt. fiz.-matem. nauk, MIAN, M., 1974 , 196 pp.

   1973
60. S. V. Bockarev, “On the absolute convergence of Fourier series of functions of bounded variation”, Soviet Math. Dokl., 14 (1973), 1669–1672  mathnet  mathscinet  mathscinet  zmath
61. S. V. Bochkarev, “On a problem og Zygmund”, Math. USSR-Izv., 7:3 (1973), 629–637  mathnet  crossref  mathscinet  zmath

   1972
62. S. V. Bockarev, “On absolute convergence of Fourier series”, Soviet Math. Dokl., 13 (1972), 225–227  mathnet  mathscinet  mathscinet  zmath
63. S. V. Bochkarev, “Asolute convergence of Fourier series with respect to complete orthonormal systems”, Russian Math. Surveys, 27:2 (1972), 55–81  mathnet  crossref  mathscinet  zmath  adsnasa

   1971
64. S. V. Bočkarev, “The absolute convergence of Fourier series”, Sibirsk. Mat. Ž., 12 (1971), 1211–1216  mathscinet
65. S. V. Bochkarev, “Absolute convergence of Fourier series over complete orthonormal systems of functions”, Math. USSR-Sb., 14:3 (1971), 429–437  mathnet  crossref  mathscinet  zmath

   1970
66. S. V. Bochkarev, “Fourier coefficients of functions of class $\mathrm{Lip} \alpha$ with respect to complete orthonormalized systems”, Math. Notes, 7:4 (1970), 239–242  mathnet  crossref  mathscinet  zmath  zmath  scopus (cited: 2)
67. S. V. Bochkarev, “On the Fourier–Walsh coefficients”, Math. USSR-Izv., 4:1 (1970), 209–214  mathnet  crossref  mathscinet  zmath

   1969
68. S. V. Bochkarev, “On series in the Haar system”, Uspekhi Mat. Nauk, 24:1(145) (1969), 189–190  mathnet  mathscinet  zmath
69. S. V. Bochkarev, “On the coefficients of Fourier series with respect to the Haar system”, Math. USSR-Sb., 9:1 (1969), 93–109  mathnet  crossref  mathscinet  zmath
70. S. V. Bochkarev, Ryady Fure po sisteme Khaara, Diss. … kand. fiz.-matem. nauk, MIAN, M., 1969 , 78 pp.

   1968
71. S. V. Bochkarev, “Series with respect to the Schauder system”, Math. Notes, 4 (1968), 763–767 (1969)  mathnet  crossref  mathscinet  zmath  zmath  scopus
72. S. V. Bochkarev, “Unconditional convergence almost everywhere of Fourier series of continuous functions in the Haar system”, Math. Notes, 4:2 (1968), 618–623  mathnet  crossref  mathscinet  zmath  scopus

   1967
73. S. V. Bochkarev, “Unconditional bases”, Math. Notes, 1:4 (1967), 261–265  mathnet  crossref  mathscinet  zmath  scopus

Presentations in Math-Net.Ru
1. Абстрактная теорема Колмогорова, приложение к метрическим пространствам и топологическим группам
S. V. Bochkarev
International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii
May 25, 2015 15:20
2. Средние Валле Пуссена рядов Фурье для квадратичного спектра и спектров степенной плотности
S. V. Bochkarev
Traditional winter session MIAN–POMI devoted to the topic "Harmonic Analysis and Theory of Functions"
December 24, 2013 16:55   
3. Средние Валле Пуссена рядов Фурье для квадратичного спектра и спектров степенной плотности
S. V. Bochkarev
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
November 21, 2012 16:00
4. Estimates for the $L_1$-norm of trigonometric sums for the spectra of power density and for a simple spectrum
S. V. Bochkarev
International conference "Approximation Theory" dedicated to the 90-th anniversary of the birth of Sergey Borisovich Stechkin (1920–1995)
August 23, 2010 13:15   
5. Multiplicative inequalities for the integral norm and problems of almost everywhere convergence of Fourier series
S. V. Bochkarev
Steklov Mathematical Institute Seminar
October 15, 2009 16:00   

Books in Math-Net.Ru
  1. S. V. Bochkarev, The method of averaging in the theory of orthogonal series and some questions in the theory of bases, Trudy Mat. Inst. Steklov., 146, ed. S. M. Nikol'skii, 1978, 88 с.
    http://mi.mathnet.ru/book1194

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