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http://dx.doi.org/10.4134/BKMS.b160365

A WEIGHTED FOURIER SERIES WITH SIGNED GOOD KERNELS  

Chan, Sony (Department of Mathematics Sogang University)
Rim, Kyung Soo (Department of Mathematics Sogang University)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.3, 2017 , pp. 935-952 More about this Journal
Abstract
It is natural to try to find a kernel such that its convolution of integrable functions converges faster than that of the $Fej{\acute{e}}r$ 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 $Ces{\grave{a}}ro$ means. In addition, we present two numerical experiments.
Keywords
Fourier series; Cesaro mean; weighted Fourier series;
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