Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain

A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn(f;t) of generalized Fourier series on a parallel hexagon domain Ω associating with three-direction partition.We prove that an operator Wn(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.