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