A weighted Fourier series with signed good kernels
Bull. Korean Math. Soc. 2017 Vol. 54, No. 3, 935-952
Published online November 1, 2016
Printed May 31, 2017
Sony Chan and Kyung Soo Rim
Sogang University, Sogang University
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
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