On some quasi-periodic approximations

Authors

  • Arnak Poghosyan Institute of Mathematics NAS RA
  • Lusine Poghosyan Institute of Mathematics NAS RA
  • Rafayel Barkhudaryan Institute of Mathematics NAS RA, Yerevan State University http://orcid.org/0000-0002-9794-9284

Keywords:

Fourier series, trigonometric interpolation, convergence acceleration, quasi-periodic approximation, quasi-periodic interpolation

Abstract

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.

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Published

2020-10-30

How to Cite

Poghosyan, A., Poghosyan, L., & Barkhudaryan, R. (2020). On some quasi-periodic approximations. Armenian Journal of Mathematics, 12(10), 1-27. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/460

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