Armenian Journal of Mathematics

On some Quasi-Periodic Approximations

Poghosyan, Arnak V. and Poghosyan, Lusine D. and Barkhudaryan, Rafayel H. (2020) On some Quasi-Periodic Approximations. Armenian Journal of Mathematics, 12 (10). pp. 1-27. ISSN 1829-1163

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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.

Item Type:Article
Uncontrolled Keywords:Fourier series, trigonometric interpolation, convergence acceleration, quasi-periodic approximation, quasi-periodic interpolation
Subjects:42-xx Fourier analysis
65-xx Numerical analysis
ID Code:867
Deposited By:Professor Anry Nersesyan
Deposited On:31 Oct 2020 11:12
Last Modified:31 Oct 2020 11:12

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