Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A WEIGHTED FOURIER SERIES WITH SIGNED GOOD KERNELS

  • Chan, Sony (Department of Mathematics Sogang University) ;
  • Rim, Kyung Soo (Department of Mathematics Sogang University)
  • Received : 2016.04.27
  • Published : 2017.05.31
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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 $Fej{\acute{e}}r$ 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.

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References

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