Armenian Journal of Mathematics

On an Over-Convergence Phenomenon for Fourier series. Basic Approach.

Nersessian, Anry (2018) On an Over-Convergence Phenomenon for Fourier series. Basic Approach. Armenian Journal of Mathematics, 10 (9). pp. 1-22. ISSN 1829-1163

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Abstract

This paper is devoted to the acceleration of the convergence of the partial sums of the classical Fourier series for the sufficiently smooth functions. Some universal and adaptive algorithms are constructed and studied. It is shown that the use of a finite number of Fourier coefficients makes it possible exact approximation of a given function from an infinite-dimensional set of quasi-polynomials. In this sense, we call the corresponding essentially nonlinear algorithms as over-convergent. The proposed algorithms are implemented using Wolfram Mathematica system. Numerical results demonstrate their effectiveness.

Item Type:Article
Subjects:42-xx Fourier analysis
65-xx Numerical analysis
ID Code:832
Deposited By:Professor Anry Nersesyan
Deposited On:26 Oct 2018 17:16
Last Modified:01 Nov 2018 18:40

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