A weighted Fourier series with signed good kernels

Sony Chan; Kyung Soo Rim

doi:10.4134/BKMS.b160365

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(3): 935-952

Online first article November 1, 2016 Printed May 31, 2017

https://doi.org/10.4134/BKMS.b160365

A weighted Fourier series with signed good kernels

Sony Chan and Kyung Soo Rim

Sogang University, Sogang University

Abstract

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Abstract

It is natural to try to find a kernel such that its convolution of integrable functions converges faster than that of the Fej\'er kernel. In this paper, we introduce a weighted Fourier partial sums which are written as the convolution of signed good kernels and prove that the weighted Fourier partial sum converges in $L^2$ much faster than that of the Ces\`aro means. In addition, we present two numerical experiments.

Keywords: Fourier series, Cesaro mean, weighted Fourier series

MSC numbers: Primary 42A99, 26A33; Secondary 42A38