Mean-Square Approximation of Complex Variable Functions by Fourier Series in the Weighted Bergman Space-Reference-Cited by-同舟云学术

Mean-Square Approximation of Complex Variable Functions by Fourier Series in the Weighted Bergman Space

Published:2017-06 Issue: Volume:9 Page:34-43
ISSN:2297-6213
Container-title:International Journal of Advanced Research in Mathematics
language:
Short-container-title:IJARM

Author:

Shabozov Mirgand Sh.¹,Saidusaynov Mukim S.²

Affiliation:

1. Academy of Sciences of the Republic of Tajikistan

2. Tajik National University

Abstract

The problem of mean-square approximation of complex variables functions regularly in some simply connected domainDc C with Fourier series by orthogonal system when the weighted functionγ: =γ(|z|) is nonnegative integrable inD, was considered. An exact convergence rate of Fourier series by orthogonal system of functions on some class of functions given by special module of continuity ofm-thorder were obtained. An exact values ofn-widthsfor specified class of functions were calculated.

Publisher

SciPress Ltd

Subject

General Medicine

Link

https://www.scipress.com/IJARM.9.34.pdf

Reference15 articles.

1. M. Sh. Shabozov, O. Sh. Shabozov, Best approximation and the value of the widths of some classes of functions in the Bergman space Bp, 1≤p≤∞, Dokl. Akad. Nauk. 410(4) (2006) 461–464.

2. M. Sh. Shabozov, O. Sh. Shabozov, On the best approximation of some classes of analytic functions in the weighted Bergman space B2, γ, Dokl. Akad. Nauk. 412(4) (2007) 466–469.

3. S.B. Vakarchuk, M. Sh. Shabozov, The widths of classes of analytic functions in a disc, Mat. Sb. 201(8) (2010) 3–22 (in Russian). Translated in: Sbornik: Mathematics. 201(8) (2010) 1091.

4. M. Sh. Shabozov, M.S. Saidusaynov, On the values of widths and the best linear method of approximation in the weighted Bergman space, Proceedings of the TSU. Natural Science. 3 (2014) 40–57. (in Russian).

5. M.S. Saidusaynov, On the values of widths and the best linear method of approximation in the weighted Bergman space, Proceedings of the TSU. Natural Science. 3 (2015) 91–104. (in Russian).