Abstract:

Linear summation method was applied to the truncations on parallel hexagon of double Fourier series associating with threedirectional coordinates. The parallel hexagon’s summation of double Fourier series of a function was putted forward. A specific convergence factor was constructed. A linear integral operator with the convergence factor was obtained. It has been proved that
 the operator converges uniformly to any given continuous double function with periodic domain Ω, where Ω is a parallel hexagon domain.

Key words: parallel hexagonal summation, convergence factor, threedirection coordinate, uniform convergence