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Vinogradov, Oleg Leonidovich

Statistics Math-Net.Ru
Total publications: 36
Scientific articles: 35
Presentations: 2

Number of views:
This page:3557
Abstract pages:8208
Full texts:2380
References:922
Associate professor
Doctor of physico-mathematical sciences (2008)
Speciality: 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.

Subject:

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.

http://www.mathnet.ru/eng/person17927
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/364553

Publications in Math-Net.Ru
2021
1. O. L. Vinogradov, “Non-saturated estimates of the Kotelnikov formula error”, Zap. Nauchn. Sem. POMI, 499 (2021),  22–37  mathnet
2020
2. 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  mathnet; St. Petersburg Math. J., 32:2 (2021), 233–260  isi  scopus
3. O. L. Vinogradov, “On the rate of decay of a Meyer scaling function”, Zap. Nauchn. Sem. POMI, 491 (2020),  52–65  mathnet
2019
4. O. L. Vinogradov, “An exact inequality of Jackson–Chernykh type for spline approximations of periodic functions”, Sibirsk. Mat. Zh., 60:3 (2019),  537–555  mathnet  elib; Siberian Math. J., 60:3 (2019), 412–428  isi  scopus
5. 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  mathnet
2018
6. 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  mathnet  mathscinet  elib; St. Petersburg Math. J., 30:5 (2019), 841–867  isi  scopus
7. 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  mathnet  mathscinet  elib; St. Petersburg Math. J., 30:2 (2019), 219–230  isi  scopus
2017
8. 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  mathnet  elib; Siberian Math. J., 58:2 (2017), 190–204  isi  elib  scopus
9. 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  mathnet; J. Math. Sci. (N. Y.), 234:3 (2018), 303–317
2016
10. 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  mathnet  mathscinet  elib; Math. Notes, 100:3 (2016), 345–351  isi  scopus
2015
11. O. L. Vinogradov, A. V. Gladkaya, “A nonperiodic analogue of the Akhiezer–Krein–Favard operators”, Zap. Nauchn. Sem. POMI, 440 (2015),  8–35  mathnet  mathscinet; J. Math. Sci. (N. Y.), 217:1 (2016), 3–22  scopus
12. O. L. Vinogradov, “Sharp Bernstein type inequalities for splines in the mean square metrics”, Zap. Nauchn. Sem. POMI, 434 (2015),  82–90  mathnet  mathscinet; J. Math. Sci. (N. Y.), 215:5 (2016), 595–600  scopus
2014
13. 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  mathnet  mathscinet  elib; St. Petersburg Math. J., 26:6 (2015), 867–879  isi
14. O. L. Vinogradov, “Sharp Estimates of Integrals in Terms of the Second Modulus of Continuity”, Mat. Zametki, 96:4 (2014),  483–495  mathnet  mathscinet  zmath  elib; Math. Notes, 96:4 (2014), 465–476  isi  elib  scopus
15. O. L. Vinogradov, “Approximation estimates for convolution classes in terms of the second modulus of continuity”, Sibirsk. Mat. Zh., 55:3 (2014),  494–508  mathnet  mathscinet  elib; Siberian Math. J., 55:3 (2014), 402–414  isi  elib  scopus
2013
16. 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  mathnet  mathscinet  zmath  elib; St. Petersburg Math. J., 25:3 (2014), 421–446  isi  scopus
17. 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  mathnet; J. Math. Sci. (N. Y.), 202:4 (2014), 526–540  scopus
2012
18. 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  mathnet  mathscinet  zmath  elib; St. Petersburg Math. J., 24:5 (2013), 691–721  isi
19. 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  mathnet  mathscinet; J. Math. Sci. (N. Y.), 193:1 (2013), 8–31  scopus
20. O. L. Vinogradov, “Sharp estimates of best approximations by deviations of Weierstrass-type integrals”, Zap. Nauchn. Sem. POMI, 401 (2012),  53–70  mathnet  mathscinet; J. Math. Sci. (N. Y.), 194:6 (2013), 628–638  scopus
2011
21. 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  mathnet; J. Math. Sci. (N. Y.), 184:6 (2012), 679–698  scopus
22. O. L. Vinogradov, “On the norms of generalized translation operators generated by Dunkl-type operators”, Zap. Nauchn. Sem. POMI, 392 (2011),  5–31  mathnet; J. Math. Sci. (N. Y.), 184:6 (2012), 663–678  scopus
23. O. L. Vinogradov, “On the norms of generalized translation operators generated by Jacobi–Dunkl operators”, Zap. Nauchn. Sem. POMI, 389 (2011),  34–57  mathnet; J. Math. Sci. (N. Y.), 182:5 (2012), 603–616  scopus
2010
24. 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  mathnet
25. 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  mathnet; J. Math. Sci. (N. Y.), 178:2 (2011), 115–131  scopus
2009
26. 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  mathnet  mathscinet  zmath  elib; Math. Notes, 85:4 (2009), 544–557  isi  scopus
2007
27. 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  mathnet  mathscinet  zmath; Siberian Math. J., 48:3 (2007), 430–445  isi  scopus
2005
28. 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  mathnet  mathscinet  zmath; St. Petersburg Math. J., 17:4 (2006), 593–633
2002
29. 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  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 124:2 (2004), 4845–4857
2001
30. O. L. Vinogradov, “On the upper bounds of Lebesgue constants for Forier–Jacobi series summation methods”, Zap. Nauchn. Sem. POMI, 282 (2001),  34–50  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 120:5 (2004), 1662–1671
1999
31. 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  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 110:5 (2002), 2944–2954
1998
32. O. L. Vinogradov, “The sharp constant in Jackson-type inequality for approximation by linear positive operators”, Zap. Nauchn. Sem. POMI, 255 (1998),  36–53  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 107:4 (2001), 3987–4001
1997
33. 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  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 101:3 (2000), 3060–3072
1996
34. 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  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 92:1 (1998), 3560–3572
1995
35. V. V. Zhuk, O. L. Vinogradov, “Parseval-type inequalities and some of their applications”, Dokl. Akad. Nauk, 341:6 (1995),  737–739  mathnet  mathscinet  zmath

2004
36. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 59:4 (2004), 771–776  isi

Presentations in Math-Net.Ru
1. О константах в неравенствах типа Джексона для модулей непрерывности высоких порядков
O. L. Vinogradov
Traditional winter session MIAN–POMI devoted to the topic "Harmonic Analysis and Theory of Functions"
December 23, 2013 11:20   
2. On some exact inequalities in approximation theory
O. L. Vinogradov
Meetings of the St. Petersburg Mathematical Society
November 11, 1997

Organisations
 
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