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

Shuyun Wang, Xuezhang Liang, Yao Fu & Xuenan Sun

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

Published online: 2021-06

Export citation
  • 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.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CMR-25-104, author = {Wang , ShuyunLiang , XuezhangFu , Yao and Sun , Xuenan}, 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:
Copy to clipboard
The citation has been copied to your clipboard