Original scientific paper

On the convergence (upper boundness) of trigonometric series

Xhevat Z. Krasniqi orcid.org/0000-0002-5032-4623 ; Department of Mathematics and Computer Sciences, University of Prishtina,Prishtinë-10 000, Republic of Kosovo

Abstract

In this paper we prove that the condition $$\sum_{k=\left[\frac{n}{2}\right]}^{2n}\frac{k^{r}\lambda _{k}}{|n-k|+1}=o(1)\, \left(=O(1)\right),$$ for $r=0,1,2,\dots,$ is necessary for the convergence of the $r-th$ derivative of the Fourier series in the $L^{1}-$metric. This condition is sufficient under some additional assumptions for Fourier coefficients. In fact, in this paper we generalize some results of A. S. Belov [1].

Keywords

Fourier coefficients; convergence of Fourier series

Hrčak ID:

44004

URI

https://hrcak.srce.hr/44004

Publication date:

9.12.2009.

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