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 - <p style="text-align: justify;">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.</p>