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
2.
S. V. Bochkarev, “An abstract Kolmogorov theorem, and an application to metric spaces and topological groups”, Sb. Math., 209:11 (2018), 1575–1602
3.
S. V. Bochkarev, “Kolmogorov’s abstract theorem: Application to metric spaces and topological groups”, Dokl. Math., 91:3 (2015), 367–370
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
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
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
7.
S. V. Bochkarev, “On a problem of Hardy for Walsh-Fourier series”, Dokl. Math., 81:3 (2010), 390–391
8.
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
9.
S. V. Bochkarev, “A Generalization of Kolmogorov's Theorem to Biorthogonal Systems”, Proc. Steklov Inst. Math., 260 (2008), 37–49
10.
S. V. Bochkarev, “Multiplicative Bounds for $L_1$-Norms of Exponential Sums”, Journal of Mathematical Sciences, 155:1 (2009), 47–56
11.
S. V. Bochkarev, “Obobschenie teoremy Kolmogorova na biortogonalnye sistemy”, Teoriya funktsii i vychislitelnye metody, Materialy mezhdunarodnoi konferentsii (Astana, 2007), Astana, 2007, 70–72
12.
S. V. Bochkarev, “Multiplicative Inequalities for the $L_1$ Norm: Applications in Analysis and Number Theory”, Proc. Steklov Inst. Math., 255 (2006), 49–64
13.
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
14.
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
15.
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
16.
S. V. Bochkarev, “Everywhere divergent Fourier-Walsh series”, Dokl. Math., 67:3 (2003), 307–310
17.
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
18.
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
19.
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
20.
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
21.
S. V. Bochkarev, “Inequalities for orthogonal series and a strengthening of the theorems of Carleman and Orlicz”, Dokl. Math., 61:2 (2000), 165–168
22.
S. V. Bochkarev, “Multiplikativnye otsenki $L_1$-normy eksponentsialnykh summ”, Metricheskaya teoriya funktsii i smezhnye voprosy analiza, Izd-vo AFTs, M., 1999, 57–68
23.
S. V. Bochkarev, “Estimation of the Fourier coefficients of functions from Lorentz spaces”, Dokl. Math., 57:3 (1998), 454–457
24.
S. V. Bochkarev, “Hausdorff–Young–Riesz Theorem in Lorentz Spaces and Multiplicative Inequalities”, Proc. Steklov Inst. Math., 219 (1997), 96–107
25.
S. V. Bochkarev, “On a method for estimating the $L_1$-norm of an exponential sum”, Proc. Steklov Inst. Math., 218 (1997), 69–71
26.
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
27.
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
28.
S. V. Bochkarev, “Convergence almost everywhere of Dini-type integrals”, Russian Acad. Sci. Dokl. Math., 49:1 (1994), 183–188
29.
S. V. Bochkarev, “Series generated by Steklov functions”, Russian Acad. Sci. Dokl. Math., 49:1 (1994), 154–159
30.
S. V. Bochkarev, “Estimates of some character sums”, Proc. Steklov Inst. Math., 207 (1995), 41–50
31.
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
32.
S. V. Bochkarev, “Rearrangements of multiplicative systems”, Soviet Math. Dokl., 43:3 (1991), 708–710 (1992)
33.
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
35.
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
36.
S. V. Bochkarev, “The conjugate Franklin system is a basis in the space of continuous functions”, Proc. Steklov Inst. Math., 180 (1989), 66–67
37.
S. V. Bochkarev, “The conjugate Franklin system is a basis in the space of continuous functions”, Soviet Math. Dokl., 32 (1985), 701–705
38.
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
39.
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
40.
S. V. Bochkarev, “Postroenie polinomialnykh bazisov v konechnomernykh prostranstvakh analiticheskikh funktsii.”, Trudy mezhdunarodnoi konferentsii po teorii priblizheniya funktsii, Nauk. dumka, Kiev, 1984, 66–69
41.
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
42.
S. V. Bochkarev, “Construction of basis in finite-dimensional spaces of analytic functions in the disk”, Soviet Math. Dokl., 25 (1982), 859–860
43.
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
44.
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
45.
S. V. Bochkarev, “Rearrangements of Fourier–Walsh series”, Math. USSR-Izv., 15:2 (1980), 259–275
46.
S. V. Bockarev, “On a majorant of the partial sums for a rearranged Walsh system”, Soviet Math. Dokl., 19 (1978), 341–342
47.
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
48.
S. V. Bochkarev, “Classes of functions and Fourier coefficients with respect to complete orthonormal systems”, Math. Notes, 20:3 (1976), 805–816
49.
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)
50.
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
52.
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
53.
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
54.
S. V. Bochkarev, “Absolute convergence of Fourier series with respect to bounded systems”, Math. Notes, 15:3 (1974), 207–211
55.
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
56.
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
57.
S. V. Bochkarev, Klassy funktsii i koeffitsienty Fure po polnym ortonormirovannym sistemam, Diss. … dokt. fiz.-matem. nauk, MIAN, M., 1974 , 196 pp.
58.
S. V. Bockarev, “On the absolute convergence of Fourier series of functions of bounded variation”, Soviet Math. Dokl., 14 (1973), 1669–1672
59.
S. V. Bochkarev, “On a problem og Zygmund”, Math. USSR-Izv., 7:3 (1973), 629–637
60.
S. V. Bockarev, “On absolute convergence of Fourier series”, Soviet Math. Dokl., 13 (1972), 225–227
61.
S. V. Bochkarev, “Asolute convergence of Fourier series with respect to complete orthonormal systems”, Russian Math. Surveys, 27:2 (1972), 55–81
62.
S. V. Bochkarev, “The absolute convergence of Fourier series”, Siberian Math. J., 12:6 (1971), 869–873
63.
S. V. Bochkarev, “Absolute convergence of Fourier series over complete orthonormal systems of functions”, Math. USSR-Sb., 14:3 (1971), 429–437
64.
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
65.
S. V. Bochkarev, “On the Fourier–Walsh coefficients”, Math. USSR-Izv., 4:1 (1970), 209–214
66.
S. V. Bochkarev, “On series in the Haar system”, Uspekhi Mat. Nauk, 24:1(145) (1969), 189–190
67.
S. V. Bochkarev, “On the coefficients of Fourier series with respect to the Haar system”, Math. USSR-Sb., 9:1 (1969), 93–109
68.
S. V. Bochkarev, Ryady Fure po sisteme Khaara, Diss. … kand. fiz.-matem. nauk, MIAN, M., 1969 , 78 pp.
69.
S. V. Bochkarev, “Series with respect to the Schauder system”, Math. Notes, 4 (1968), 763–767 (1969)
70.
S. V. Bochkarev, “Unconditional convergence almost everywhere of Fourier series of continuous functions in the Haar system”, Math. Notes, 4:2 (1968), 618–623
71.
S. V. Bochkarev, “Unconditional bases”, Math. Notes, 1:4 (1967), 261–265
72.
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
73.
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
74.
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
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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