01.01.01 (Real analysis, complex analysis, and functional analysis)
Keywords:
convergence and unconditional convergence almost everywhere,
Walsh system,
absolute convergence,
classical and general orthogonal systems,
multiplicative inequalities,
exponential sums.
Trigonometic and orthogonal series, functional spaces, bases, almost everywhere convergence, exponential sums, BMO and Hardy spaces, multiplicative systems.
Main publications:
S. V. Bochkarev, “A Generalization of Kolmogorov's Theorem to Biorthogonal Systems”, Proc. Steklov Inst. Math., 260 (2008), 37–49
S. V. Bochkarev, “Multiplicative Inequalities for the $L_1$ Norm: Applications in Analysis and Number Theory”, Proc. Steklov Inst. Math., 255 (2006), 49–64
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
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
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
S. V. Bochkarev, “Inequalities for Orthogonal Series and a Strengthening of the Carleman–Olevskii Theorem for Complete Orthonormal Systems”, Proc. Steklov Inst. Math., 312 (2021), 104–123
2018
2.
S. V. Bochkarev, “An abstract Kolmogorov theorem, and an application to metric spaces and topological groups”, Sb. Math., 209:11 (2018), 1575–1602
2015
3.
S. V. Bochkarev, “Kolmogorov’s abstract theorem: Application to metric spaces and topological groups”, Dokl. Math., 91:3 (2015), 367–370
2014
4.
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
2013
5.
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
2012
6.
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
7.
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
8.
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
2010
9.
S. V. Bochkarev, “On a problem of Hardy for Walsh-Fourier series”, Dokl. Math., 81:3 (2010), 390–391
2008
10.
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
11.
S. V. Bochkarev, “A Generalization of Kolmogorov's Theorem to Biorthogonal Systems”, Proc. Steklov Inst. Math., 260 (2008), 37–49
2009
12.
S. V. Bochkarev, “Multiplicative Bounds for $L_1$-Norms of Exponential Sums”, Journal of Mathematical Sciences, 155:1 (2009), 47–56
2007
13.
S. V. Bochkarev, “Obobschenie teoremy Kolmogorova na biortogonalnye sistemy”, Teoriya funktsii i vychislitelnye metody, Materialy mezhdunarodnoi konferentsii (Astana, 2007), Astana, 2007, 70–72
2006
14.
S. V. Bochkarev, “Multiplicative Inequalities for the $L_1$ Norm: Applications in Analysis and Number Theory”, Proc. Steklov Inst. Math., 255 (2006), 49–64
2005
15.
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
16.
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
2004
17.
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
2003
18.
S. V. Bochkarev, “Everywhere divergent Fourier-Walsh series”, Dokl. Math., 67:3 (2003), 307–310
19.
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
2002
20.
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
2001
21.
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
2000
22.
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
23.
S. V. Bochkarev, “Inequalities for orthogonal series and a strengthening of the theorems of Carleman and Orlicz”, Dokl. Math., 61:2 (2000), 165–168
1999
24.
S. V. Bochkarev, “Multiplikativnye otsenki $L_1$-normy eksponentsialnykh summ”, Metricheskaya teoriya funktsii i smezhnye voprosy analiza, Izd-vo AFTs, M., 1999, 57–68
1998
25.
S. V. Bochkarev, “Estimation of the Fourier coefficients of functions from Lorentz spaces”, Dokl. Math., 57:3 (1998), 454–457
1997
26.
S. V. Bochkarev, “Hausdorff–Young–Riesz Theorem in Lorentz Spaces and Multiplicative Inequalities”, Proc. Steklov Inst. Math., 219 (1997), 96–107
27.
S. V. Bochkarev, “On a method for estimating the $L_1$-norm of an exponential sum”, Proc. Steklov Inst. Math., 218 (1997), 69–71
1995
28.
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
29.
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
30.
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
1994
31.
S. V. Bochkarev, “Convergence almost everywhere of Dini-type integrals”, Russian Acad. Sci. Dokl. Math., 49:1 (1994), 183–188
32.
S. V. Bochkarev, “Series generated by Steklov functions”, Russian Acad. Sci. Dokl. Math., 49:1 (1994), 154–159
1995
33.
S. V. Bochkarev, “Estimates of some character sums”, Proc. Steklov Inst. Math., 207 (1995), 41–50
1994
34.
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
1991
35.
S. V. Bochkarev, “Rearrangements of multiplicative systems”, Soviet Math. Dokl., 43:3 (1991), 708–710 (1992)
1990
36.
S. V. Bochkarev, “Rearrangements of periodic multiplicative orthogonal series”, Colloq. Math., 60/61:1 (1990), 291–299
S. V. Bochkarev, “Bases in functional spaces and the Franklin system”, Proc. Steklov Inst. Math., 190 (1992), 19–37
1987
38.
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
1989
39.
S. V. Bochkarev, “The conjugate Franklin system is a basis in the space of continuous functions”, Proc. Steklov Inst. Math., 180 (1989), 66–67
1985
40.
S. V. Bochkarev, “The conjugate Franklin system is a basis in the space of continuous functions”, Soviet Math. Dokl., 32 (1985), 701–705
1987
41.
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
1985
42.
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
1984
43.
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
44.
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
1982
45.
S. V. Bochkarev, “Construction of basis in finite-dimensional spaces of analytic functions in the disk”, Soviet Math. Dokl., 25 (1982), 859–860
46.
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
47.
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
1980
48.
S. V. Bochkarev, “Rearrangements of Fourier–Walsh series”, Math. USSR-Izv., 15:2 (1980), 259–275
1978
49.
S. V. Bockarev, “On a majorant of the partial sums for a rearranged Walsh system”, Soviet Math. Dokl., 19 (1978), 341–342
1980
50.
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
1976
51.
S. V. Bochkarev, “Classes of functions and Fourier coefficients with respect to complete orthonormal systems”, Math. Notes, 20:3 (1976), 805–816
1975
52.
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)
53.
S. V. Bočkarev, “Some inequalities for Franklin series”, Anal. Math., 1:4 (1975), 249–257
S. V. Bockarev, “Logarithmic growth of arithmetic means of Lebesgue functions of bounded orthonormal systems”, Soviet Math. Dokl., 16 (1975), 799–802
55.
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
1974
56.
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
57.
S. V. Bochkarev, “Absolute convergence of Fourier series with respect to bounded systems”, Math. Notes, 15:3 (1974), 207–211
58.
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
59.
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
60.
S. V. Bochkarev, Klassy funktsii i koeffitsienty Fure po polnym ortonormirovannym sistemam, Diss. … dokt. fiz.-matem. nauk, MIAN, M., 1974 , 196 pp.
1973
61.
S. V. Bockarev, “On the absolute convergence of Fourier series of functions of bounded variation”, Soviet Math. Dokl., 14 (1973), 1669–1672
62.
S. V. Bochkarev, “On a problem og Zygmund”, Math. USSR-Izv., 7:3 (1973), 629–637
1972
63.
S. V. Bockarev, “On absolute convergence of Fourier series”, Soviet Math. Dokl., 13 (1972), 225–227
64.
S. V. Bochkarev, “Asolute convergence of Fourier series with respect to complete orthonormal systems”, Russian Math. Surveys, 27:2 (1972), 55–81
1971
65.
S. V. Bochkarev, “The absolute convergence of Fourier series”, Siberian Math. J., 12:6 (1971), 869–873
66.
S. V. Bochkarev, “Absolute convergence of Fourier series over complete orthonormal systems of functions”, Math. USSR-Sb., 14:3 (1971), 429–437
1970
67.
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
68.
S. V. Bochkarev, “On the Fourier–Walsh coefficients”, Math. USSR-Izv., 4:1 (1970), 209–214
1969
69.
S. V. Bochkarev, “On series in the Haar system”, Uspekhi Mat. Nauk, 24:1(145) (1969), 189–190
70.
S. V. Bochkarev, “On the coefficients of Fourier series with respect to the Haar system”, Math. USSR-Sb., 9:1 (1969), 93–109
71.
S. V. Bochkarev, Ryady Fure po sisteme Khaara, Diss. … kand. fiz.-matem. nauk, MIAN, M., 1969 , 78 pp.
1968
72.
S. V. Bochkarev, “Series with respect to the Schauder system”, Math. Notes, 4 (1968), 763–767 (1969)
73.
S. V. Bochkarev, “Unconditional convergence almost everywhere of Fourier series of continuous functions in the Haar system”, Math. Notes, 4:2 (1968), 618–623
1967
74.
S. V. Bochkarev, “Unconditional bases”, Math. Notes, 1:4 (1967), 261–265
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
2021
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