Izvorni znanstveni članak
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
Sažetak
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].
Ključne riječi
Fourier coefficients; convergence of Fourier series
Hrčak ID:
44004
URI
Datum izdavanja:
9.12.2009.
Posjeta: 1.411 *