东北数学（英文版）
東北數學（英文版）
동북수학（영문판）
NORTHEASTERN MATHEMATICAL JOURNAL
2006年
1期
99-104
,共6页
trigonometric summation polynomial%uniform convergence%the best convergence order%saturation order
A new family of trigonometric summation polynomials, Gn,r(f; θ), of Bernstein type is constructed. In contrast to other trigonometric summation polynomials, the convergence properties of the new polynomials are superior to others.It is proved that Gn,r(f; θ) converges to arbitrary continuous functions with period 2π uniformly on (-∞, +∞) as n →∞. In particular, Gn,r(f; θ) has the best convergence order, and its saturation order is 1/n2r+4.
