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A weighted Fourier series with signed good kernels

임경수|Sony Chan
대한수학회 (The Korean Mathematical Society)|2017.05|대한수학회보 (Bulletin of the KMS)|제54권 제3호|pp. 935-952

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참고문헌

키워드

Fourier seriesCesaro meanweighted Fourier series
주제분류수학

초록

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.

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.

참고문헌 (17)

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