On some quasi-periodic approximations

Armenian Journal of Mathematics

article

Arnak Poghosyan¹  Lusine Poghosyan¹  Rafayel Barkhudaryan² 

[1] Institute of Mathematics NAS RA;Institute of Mathematics NAS RA, Yerevan State University

关键词: Fourier series;    trigonometric interpolation;    convergence acceleration;    quasi-periodic approximation;    quasi-periodic interpolation;   

DOI  :  10.52737/18291163-2020.12.10-1-27

学科分类：环境科学（综合）

来源: National Academy of Sciences of the Republic of Armenia

【 摘 要 】

Trigonometric approximation or interpolation of a non-smooth function on a finite interval has poor convergence properties. This is especially true for discontinuous functions. The case of infinitely differentiable but non-periodic functions with discontinuous periodic extensions onto the real axis has attracted interest from many researchers. In a series of works, we discussed an approach based on quasi-periodic trigonometric basis functions whose periods are slightly bigger than the length of the approximation interval. We proved validness of the approach for trigonometric interpolations. In this paper, we apply those ideas to classical Fourier expansions.

【 授权许可】

CC BY