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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.
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참고문헌 (19)
참고문헌 신청
Fourier series / J. Math. Soc. Japan 10 (1) : 55 ~ 63
A. Zygmund / 2002 / Trigonometric Series / Camabridge University Press
D. Borwein / 1967 / On Riesz and generalised Ces`aro summability of arbitrary positive order / Math. Zeitschr 99 : 171 ~ 177
F. Weisz / 1996 / Ces`aro summability of multi-dimensional trigonometric-Fourier series / J. Math. Anal. Appl 204 (2) : 419 ~ 431
F. Weisz / 2012 / Ces`aro-summability of higher-dimensional Fourier series / Ann. Univ. Sci. Bu-dapest. Sect. Comput 37 : 47 ~ 64
A. Zygmund / 2002 / Trigonometric Series / Camabridge University Press
D. Borwein / 1967 / On Riesz and generalised Ces`aro summability of arbitrary positive order / Math. Zeitschr 99 : 171 ~ 177
F. Weisz / 1996 / Ces`aro summability of multi-dimensional trigonometric-Fourier series / J. Math. Anal. Appl 204 (2) : 419 ~ 431
F. Weisz / 2012 / Ces`aro-summability of higher-dimensional Fourier series / Ann. Univ. Sci. Bu-dapest. Sect. Comput 37 : 47 ~ 64
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