|
Estimates for the rate of convergence of Fourier series in the Sobolev orthogonal functional system generated by the Walsh system
M. G. Magomed-Kasumov Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
Abstract:
For functions from the Sobolev spaces $W^r_{L^p}$, we obtain several estimates for the rate of approximation by partial sums of Fourier series in Sobolev-type system generated by Walsh system: pointwise estimates; uniform estimates in terms of the integral modulus of continuity for the derivative; estimates in the metric of the Sobolev space $W^r_{L^p}$ in terms of the best approximations.
Keywords:
Sobolev inner product, Walsh system, approximation properties, Sobolev space, Fourier series.
Citation:
M. G. Magomed-Kasumov, “Estimates for the rate of convergence of Fourier series in the Sobolev orthogonal functional system generated by the Walsh system”, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 200, VINITI, Moscow, 2021, 73–80
Linking options:
https://www.mathnet.ru/eng/into902 https://www.mathnet.ru/eng/into/v200/p73
|
Statistics & downloads: |
Abstract page: | 101 | Full-text PDF : | 40 | References: | 14 |
|