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, “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
2.
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
3.
S. V. Bochkarev, “Asolute convergence of Fourier series with respect to complete orthonormal systems”, Russian Math. Surveys, 27:2 (1972), 55–81
4.
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
5.
S. V. Bočkarev, “Some inequalities for Franklin series”, Anal. Math., 1:4 (1975), 249–257
S. V. Bochkarev, “On a method for estimating the $L_1$-norm of an exponential sum”, Proc. Steklov Inst. Math., 218 (1997), 69–71
7.
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
8.
S. V. Bochkarev, “Hausdorff–Young–Riesz Theorem in Lorentz Spaces and Multiplicative Inequalities”, Proc. Steklov Inst. Math., 219 (1997), 96–107
9.
S. V. Bochkarev, “On a problem og Zygmund”, Math. USSR-Izv., 7:3 (1973), 629–637
10.
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
11.
S. V. Bockarev, “Logarithmic growth of arithmetic means of Lebesgue functions of bounded orthonormal systems”, Soviet Math. Dokl., 16 (1975), 799–802
12.
S. V. Bochkarev, “Absolute convergence of Fourier series with respect to bounded systems”, Math. Notes, 15:3 (1974), 207–211
13.
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
14.
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
15.
S. V. Bochkarev, “Rearrangements of Fourier–Walsh series”, Math. USSR-Izv., 15:2 (1980), 259–275
16.
S. V. Bochkarev, “Multiplicative Inequalities for the $L_1$ Norm: Applications in Analysis and Number Theory”, Proc. Steklov Inst. Math., 255 (2006), 49–64
17.
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
18.
S. V. Bochkarev, “On the coefficients of Fourier series with respect to the Haar system”, Math. USSR-Sb., 9:1 (1969), 93–109
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
20.
S. V. Bochkarev, “Bases in functional spaces and the Franklin system”, Proc. Steklov Inst. Math., 190 (1992), 19–37
21.
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
22.
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
23.
S. V. Bockarev, “On a majorant of the partial sums for a rearranged Walsh system”, Soviet Math. Dokl., 19 (1978), 341–342
24.
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
25.
S. V. Bochkarev, “Series with respect to the Schauder system”, Math. Notes, 4 (1968), 763–767 (1969)
26.
S. V. Bochkarev, “Unconditional convergence almost everywhere of Fourier series of continuous functions in the Haar system”, Math. Notes, 4:2 (1968), 618–623
27.
S. V. Bochkarev, “Unconditional bases”, Math. Notes, 1:4 (1967), 261–265
28.
S. V. Bochkarev, “A Generalization of Kolmogorov's Theorem to Biorthogonal Systems”, Proc. Steklov Inst. Math., 260 (2008), 37–49
29.
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
30.
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
31.
S. V. Bochkarev, “Construction of basis in finite-dimensional spaces of analytic functions in the disk”, Soviet Math. Dokl., 25 (1982), 859–860
32.
S. V. Bochkarev, “An abstract Kolmogorov theorem, and an application to metric spaces and topological groups”, Sb. Math., 209:11 (2018), 1575–1602
33.
S. V. Bochkarev, “Kolmogorov’s abstract theorem: Application to metric spaces and topological groups”, Dokl. Math., 91:3 (2015), 367–370
34.
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
35.
S. V. Bochkarev, “Multiplicative Bounds for $L_1$-Norms of Exponential Sums”, Journal of Mathematical Sciences, 155:1 (2009), 47–56
36.
S. V. Bochkarev, “Everywhere divergent Fourier-Walsh series”, Dokl. Math., 67:3 (2003), 307–310
37.
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
38.
S. V. Bochkarev, “Inequalities for orthogonal series and a strengthening of the theorems of Carleman and Orlicz”, Dokl. Math., 61:2 (2000), 165–168
39.
S. V. Bochkarev, “Estimation of the Fourier coefficients of functions from Lorentz spaces”, Dokl. Math., 57:3 (1998), 454–457
40.
S. V. Bochkarev, “Estimates of some character sums”, Proc. Steklov Inst. Math., 207 (1995), 41–50
41.
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
42.
S. V. Bochkarev, “Rearrangements of multiplicative systems”, Soviet Math. Dokl., 43:3 (1991), 708–710 (1992)
43.
S. V. Bochkarev, “Rearrangements of periodic multiplicative orthogonal series”, Colloq. Math., 60/61:1 (1990), 291–299
S. V. Bockarev, “On absolute convergence of Fourier series”, Soviet Math. Dokl., 13 (1972), 225–227
45.
S. V. Bochkarev, “The absolute convergence of Fourier series”, Siberian Math. J., 12:6 (1971), 869–873
46.
S. V. Bochkarev, “Absolute convergence of Fourier series over complete orthonormal systems of functions”, Math. USSR-Sb., 14:3 (1971), 429–437
47.
S. V. Bochkarev, “On the Fourier–Walsh coefficients”, Math. USSR-Izv., 4:1 (1970), 209–214
48.
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
49.
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
50.
S. V. Bochkarev, “On a problem of Hardy for Walsh-Fourier series”, Dokl. Math., 81:3 (2010), 390–391
51.
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
52.
S. V. Bochkarev, “Obobschenie teoremy Kolmogorova na biortogonalnye sistemy”, Teoriya funktsii i vychislitelnye metody, Materialy mezhdunarodnoi konferentsii (Astana, 2007), Astana, 2007, 70–72
53.
S. V. Bochkarev, “Multiplikativnye otsenki $L_1$-normy eksponentsialnykh summ”, Metricheskaya teoriya funktsii i smezhnye voprosy analiza, Izd-vo AFTs, M., 1999, 57–68
54.
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
55.
S. V. Bochkarev, “Convergence almost everywhere of Dini-type integrals”, Russian Acad. Sci. Dokl. Math., 49:1 (1994), 183–188
56.
S. V. Bochkarev, “Series generated by Steklov functions”, Russian Acad. Sci. Dokl. Math., 49:1 (1994), 154–159
57.
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
58.
S. V. Bochkarev, “The conjugate Franklin system is a basis in the space of continuous functions”, Proc. Steklov Inst. Math., 180 (1989), 66–67
59.
S. V. Bochkarev, “The conjugate Franklin system is a basis in the space of continuous functions”, Soviet Math. Dokl., 32 (1985), 701–705
60.
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
61.
S. V. Bochkarev, “Postroenie polinomialnykh bazisov v konechnomernykh prostranstvakh analiticheskikh funktsii.”, Trudy mezhdunarodnoi konferentsii po teorii priblizheniya funktsii, Nauk. dumka, Kiev, 1984, 66–69
62.
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
63.
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
64.
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
65.
S. V. Bochkarev, “Classes of functions and Fourier coefficients with respect to complete orthonormal systems”, Math. Notes, 20:3 (1976), 805–816
66.
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)
67.
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
68.
S. V. Bochkarev, Klassy funktsii i koeffitsienty Fure po polnym ortonormirovannym sistemam, Diss. … dokt. fiz.-matem. nauk, MIAN, M., 1974 , 196 pp.
69.
S. V. Bockarev, “On the absolute convergence of Fourier series of functions of bounded variation”, Soviet Math. Dokl., 14 (1973), 1669–1672
70.
S. V. Bochkarev, “On series in the Haar system”, Uspekhi Mat. Nauk, 24:1(145) (1969), 189–190
71.
S. V. Bochkarev, Ryady Fure po sisteme Khaara, Diss. … kand. fiz.-matem. nauk, MIAN, M., 1969 , 78 pp.
72.
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
73.
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
74.
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
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