01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
19.08.1972
E-mail:
Keywords:
extremal problems of approximation theory; linear methods of approximation; Fourier series; orthogonal polynomials; best constants; inequalities for derivatives; formulas of numerical differentiation; moduli of continuity.
Scientific interests are mainly connected with extremal problems of approximation theory. Several inequalities for the second modulus of continuity of periodical functions were established. These inequalities are sharp in the uniform metric. The sharp estimate for Rogozinski sums deviation by the second modulus of continuity was obtained. The sharp constant in Jackson inequality with the first modulus of continuity for approximation by linear positive operators was found. The limits and supremums of Lebesgue constants sequences for several summation methods defined by multiplier function were found for some Fourier–Jacobi series. Several extremal problems were solved jointly with V.V.Zhuk. The following problems were stidied: sharp Jackson and Kolmogorov-type inequalities for moduli of continuity of odd order derivatives with different step, the smallest step of the modulus of continuity in Jackson-type inequalities, Jackson-type inequalities for different metrics, sharp inequalities for trigonometrical polynomials and their connection with numerical differentiation-type formulas, sharp estimates for the deviation of mean value of periodical function and quadrature formulas errors in the terms of moduli of continuity of high orders.
Biography
Graduated from Faculty of Mathematics and Mechanics of Saint-Petersburg State University in 1994 (department of mathematical analysis). Cand.Sci. thesis was defended in 1996. A list of my works contain 35 titles.
Main publications:
Vinogradov O. L. Tochnoe neravenstvo dlya otkloneniya summ Rogozinskogo i vtorogo modulya nepreryvnosti v prostranstve nepreryvnykh periodicheskikh funktsii // Zapiski nauchnykh seminarov POMI, 1997. T. 247. S. 26–45.
Vinogradov O. L. Tochnaya postoyannaya v neravenstve tipa Dzheksona dlya priblizheniya lineinymi polozhitelnymi operatorami // Zapiski nauchnykh seminarov POMI, 1998. T. 255. S. 36–53.
Vinogradov O. L. Predel konstant Lebega metodov summirovaniya ryadov Fure–Lezhandra, zadavaemykh funktsiei mnozhitelei // Zapiski nauchnykh seminarov POMI, 1999. T. 262. S. 71–89.
Vinogradov O. L., Zhuk V. V. Tochnye otsenki pogreshnostei formul tipa chislennogo differentsirovaniya na trigonometricheskikh mnogochlenakh // Problemy matematicheskogo analiza. Vypusk 21, 2000. S. 68–109.
Vinogradov O. L., Zhuk V. V. Tochnye neravenstva tipa Dzheksona dlya differentsiruemykh funktsii i minimizatsiya shaga modulya nepreryvnosti // Trudy Sankt–Peterburgskogo matematicheskogo obschestva, 2000. T. 8. S. 29–51.
O. L. Vinogradov, “Direct and inverse theorems of approximation theory in Lebesgue spaces with Muckenhoupt weights”, Ufimsk. Mat. Zh., 15:4 (2023), 42–60; Ufa Math. J., 15:4 (2023), 42–61
O. L. Vinogradov, “On constants in abstract inverse theorems of approximation theory”, Algebra i Analiz, 34:4 (2022), 22–46; St. Petersburg Math. J., 34:4 (2023), 573–589
O. L. Vinogradov, “Sharp Bernstein Inequalities for Jacobi–Dunkl Operators”, Mat. Zametki, 112:5 (2022), 770–783; Math. Notes, 112:5 (2022), 763–775
7.
O. L. Vinogradov, “On the constants in the inverse theorems for the norms of derivatives”, Sibirsk. Mat. Zh., 63:3 (2022), 531–544; Siberian Math. J., 63:3 (2022), 438–450
O. L. Vinogradov, “On the constants in the inverse theorems for the first derivative”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8:4 (2021), 559–571; Vestn. St. Petersbg. Univ., Math., 8:4 (2021), 334–344
O. L. Vinogradov, “Non-saturated estimates of the Kotelnikov formula error”, Zap. Nauchn. Sem. POMI, 499 (2021), 22–37
2020
11.
O. L. Vinogradov, “Classes of convolutions with a singular family of kernels: Sharp constants for approximation by spaces of shifts”, Algebra i Analiz, 32:2 (2020), 45–84; St. Petersburg Math. J., 32:2 (2021), 233–260
O. L. Vinogradov, A. Yu. Ulitskaya, “Optimal subspaces for mean square approximation of classes of differentiable functions on a segment”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:3 (2020), 404–417; Vestn. St. Petersbg. Univ., Math., 7:3 (2020), 270–281
13.
O. L. Vinogradov, “Sharp jackson - Chernykh type inequality for spline approximations on the line”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:1 (2020), 15–27; Vestn. St. Petersbg. Univ., Math., 7:1 (2020), 10–19
O. L. Vinogradov, “An exact inequality of Jackson–Chernykh type for spline approximations of periodic functions”, Sibirsk. Mat. Zh., 60:3 (2019), 537–555; Siberian Math. J., 60:3 (2019), 412–428
O. L. Vinogradov, “Analogs of the Riesz identity, and sharp inequalities for derivatives and differences of splines in the integral metric”, Zap. Nauchn. Sem. POMI, 480 (2019), 86–102
2018
17.
O. L. Vinogradov, “Sharp constants for approximations of convolution classes with an integrable kernel by spaces of shifts”, Algebra i Analiz, 30:5 (2018), 112–148; St. Petersburg Math. J., 30:5 (2019), 841–867
O. L. Vinogradov, A. V. Gladkaya, “Entire functions with the least deviation from zero in generalized Orlicz classes”, Algebra i Analiz, 30:2 (2018), 97–113; St. Petersburg Math. J., 30:2 (2019), 219–230
O. L. Vinogradov, “Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions”, Sibirsk. Mat. Zh., 58:2 (2017), 251–269; Siberian Math. J., 58:2 (2017), 190–204
O. L. Vinogradov, A. V. Gladkaya, “Sharp estimates of linear approximations by nonperiodic splines in terms of linear combinations of moduli of continuity”, Zap. Nauchn. Sem. POMI, 456 (2017), 55–76; J. Math. Sci. (N. Y.), 234:3 (2018), 303–317
2016
21.
P. A. Andrianov, O. L. Vinogradov, “On the Constant and Step in Jackson's Inequality for Best Approximations by Trigonometric Polynomials and by Haar Polynomials”, Mat. Zametki, 100:3 (2016), 323–330; Math. Notes, 100:3 (2016), 345–351
2015
22.
O. L. Vinogradov, A. V. Gladkaya, “A nonperiodic analogue of the Akhiezer–Krein–Favard operators”, Zap. Nauchn. Sem. POMI, 440 (2015), 8–35; J. Math. Sci. (N. Y.), 217:1 (2016), 3–22
O. L. Vinogradov, “Sharp Bernstein type inequalities for splines in the mean square metrics”, Zap. Nauchn. Sem. POMI, 434 (2015), 82–90; J. Math. Sci. (N. Y.), 215:5 (2016), 595–600
2014
24.
O. L. Vinogradov, A. V. Gladkaya, “Entire functions with the least deviation from zero in the uniform and the integral metrics with a weight”, Algebra i Analiz, 26:6 (2014), 10–28; St. Petersburg Math. J., 26:6 (2015), 867–879
O. L. Vinogradov, “Sharp Estimates of Integrals in Terms of the Second Modulus of Continuity”, Mat. Zametki, 96:4 (2014), 483–495; Math. Notes, 96:4 (2014), 465–476
26.
O. L. Vinogradov, “Approximation estimates for convolution classes in terms of the second modulus of continuity”, Sibirsk. Mat. Zh., 55:3 (2014), 494–508; Siberian Math. J., 55:3 (2014), 402–414
2013
27.
O. L. Vinogradov, V. V. Zhuk, “Estimates for functionals with a known finite set of moments in terms of high order moduli of continuity in the spaces of functions defined on the segment”, Algebra i Analiz, 25:3 (2013), 86–120; St. Petersburg Math. J., 25:3 (2014), 421–446
O. L. Vinogradov, V. V. Zhuk, “Estimates of functionals by the second moduli of continuity of even derivatives”, Zap. Nauchn. Sem. POMI, 416 (2013), 70–90; J. Math. Sci. (N. Y.), 202:4 (2014), 526–540
O. L. Vinogradov, V. V. Zhuk, “Estimates for functional with a known finite set of moments in terms of moduli of continuity and behaviour of constants in the Jackson-type inequalities”, Algebra i Analiz, 24:5 (2012), 1–43; St. Petersburg Math. J., 24:5 (2013), 691–721
O. L. Vinogradov, “Sharp estimates of best approximations in terms of holomorphic functions of Weierstrass-type operators”, Zap. Nauchn. Sem. POMI, 404 (2012), 18–60; J. Math. Sci. (N. Y.), 193:1 (2013), 8–31
31.
O. L. Vinogradov, “Sharp estimates of best approximations by deviations of Weierstrass-type integrals”, Zap. Nauchn. Sem. POMI, 401 (2012), 53–70; J. Math. Sci. (N. Y.), 194:6 (2013), 628–638
O. L. Vinogradov, V. V. Zhuk, “Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences”, Zap. Nauchn. Sem. POMI, 392 (2011), 32–66; J. Math. Sci. (N. Y.), 184:6 (2012), 679–698
O. L. Vinogradov, “On the norms of generalized translation operators generated by Dunkl-type operators”, Zap. Nauchn. Sem. POMI, 392 (2011), 5–31; J. Math. Sci. (N. Y.), 184:6 (2012), 663–678
O. L. Vinogradov, “On the norms of generalized translation operators generated by Jacobi–Dunkl operators”, Zap. Nauchn. Sem. POMI, 389 (2011), 34–57; J. Math. Sci. (N. Y.), 182:5 (2012), 603–616
O. L. Vinogradov, V. V. Zhuk, “The rate of decrease of constants in Jackson type inequalities in dependence of the order of modulus of continuity”, Zap. Nauchn. Sem. POMI, 383 (2010), 33–52
O. L. Vinogradov, V. V. Zhuk, “Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means”, Zap. Nauchn. Sem. POMI, 383 (2010), 5–32; J. Math. Sci. (N. Y.), 178:2 (2011), 115–131
O. L. Vinogradov, “Sharp Inequalities for Approximations of Classes of Periodic Convolutions by Odd-Dimensional Subspaces of Shifts”, Mat. Zametki, 85:4 (2009), 569–584; Math. Notes, 85:4 (2009), 544–557
O. L. Vinogradov, “Sharp error estimates for the numerical differentiation formulas on the classes of entire functions of exponential type”, Sibirsk. Mat. Zh., 48:3 (2007), 538–555; Siberian Math. J., 48:3 (2007), 430–445
O. L. Vinogradov, “Sharp Jackson type inequalities for approximation of classes of convolutions by entire functions of finite degree”, Algebra i Analiz, 17:4 (2005), 59–114; St. Petersburg Math. J., 17:4 (2006), 593–633
O. L. Vinogradov, V. V. Zhuk, “Sharp Kolmogorov-type inequalities for moduli of continuity and best approximations by trigonometric polynomials and splines”, Zap. Nauchn. Sem. POMI, 290 (2002), 5–26; J. Math. Sci. (N. Y.), 124:2 (2004), 4845–4857
O. L. Vinogradov, “On the upper bounds of Lebesgue constants for Forier–Jacobi series summation methods”, Zap. Nauchn. Sem. POMI, 282 (2001), 34–50; J. Math. Sci. (N. Y.), 120:5 (2004), 1662–1671
O. L. Vinogradov, “The limit of the Lebesgue constants of summation methods of Fourier–Legendre series determined by a multiplier function”, Zap. Nauchn. Sem. POMI, 262 (1999), 71–89; J. Math. Sci. (New York), 110:5 (2002), 2944–2954
1998
43.
O. L. Vinogradov, “The sharp constant in Jackson-type inequality for approximation by linear positive operators”, Zap. Nauchn. Sem. POMI, 255 (1998), 36–53; J. Math. Sci. (New York), 107:4 (2001), 3987–4001
1997
44.
O. L. Vinogradov, “The sharp constant in the estimate of the Rogozinski sums deviation in terms of the second modulus of continuity
in the space of continuous periodic functions”, Zap. Nauchn. Sem. POMI, 247 (1997), 26–45; J. Math. Sci. (New York), 101:3 (2000), 3060–3072
O. L. Vinogradov, “Sharp inequalities for the second modulus of continuity of periodic functions and of functions extended from the segment”, Zap. Nauchn. Sem. POMI, 232 (1996), 33–49; J. Math. Sci. (New York), 92:1 (1998), 3560–3572
V. V. Zhuk, O. L. Vinogradov, “Parseval-type inequalities and some of their applications”, Dokl. Akad. Nauk, 341:6 (1995), 737–739
2004
47.
V. M. Babich, A. M. Vershik, V. S. Videnskii, O. L. Vinogradov, I. K. Daugavet, N. Yu. Dodonov, V. V. Zhuk, B. M. Makarov, A. N. Podkorutov, Yu. G. Reshetnyak, M. A. Skopina, V. L. Fainshmidt, V. P. Havin, N. A. Shirokov, “Garal'd Isidorovich Natanson (obituary)”, Uspekhi Mat. Nauk, 59:4(358) (2004), 181–185; Russian Math. Surveys, 59:4 (2004), 771–776
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