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.
UDC: 517.5, 517.518.8, 519.644, 519.65 MSC: 41Axx, 42Axx, 42C10
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.
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.
