Year: 2009
Author: Shuyun Wang, Xuezhang Liang, Yao Fu, Xuenan Sun
Communications in Mathematical Research , Vol. 25 (2009), Iss. 2 : pp. 104–114
Abstract
A new Rogosinski-type kernel function is constructed using kernel function of partial sums $S_n(f;t)$ of generalized Fourier series on a parallel hexagon domain $Ω$ associating with three-direction partition. We prove that an operator $W_n(f;t)$ with the new kernel function converges uniformly to any continuous function $f(t) ∈ C_∗(Ω)$ (the space of all continuous functions with period $Ω$) on $Ω$. Moreover, the convergence order of the operator is presented for the smooth approached function.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-CMR-19300
Communications in Mathematical Research , Vol. 25 (2009), Iss. 2 : pp. 104–114
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: three-direction coordinate kernel function generalized Fourier series uniform convergence.