Volume 25, Issue 2
Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain

Commun. Math. Res., 25 (2009), pp. 104-114.

Published online: 2021-06

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• 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.

• Keywords

three-direction coordinate, kernel function, generalized Fourier series, uniform convergence.

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@Article{CMR-25-104, author = {Shuyun and Wang and and 18120 and and Shuyun Wang and Xuezhang and Liang and and 18121 and and Xuezhang Liang and Yao and Fu and and 18122 and and Yao Fu and Xuenan and Sun and and 18123 and and Xuenan Sun}, title = {Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {2}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19300.html} }
TY - JOUR T1 - Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain AU - Wang , Shuyun AU - Liang , Xuezhang AU - Fu , Yao AU - Sun , Xuenan JO - Communications in Mathematical Research VL - 2 SP - 104 EP - 114 PY - 2021 DA - 2021/06 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19300.html KW - three-direction coordinate, kernel function, generalized Fourier series, uniform convergence. AB -

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.

ShuyunWang, XuezhangLiang, YaoFu & XuenanSun. (2021). Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain. Communications in Mathematical Research . 25 (2). 104-114. doi:
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