复空间内三角级数的一致收敛性(英文)

Uniform Convergence of Trigonometric Series in the Complex Space

对三角级数的系数单调性在复数意义下做出推广,并获得了三角级数在复空间内一致收敛的充分必要条件.结论在实系数的意义下推广了Chaundy与Jolliffe的经典结果.

In this paper, we consider numerical and trigonometric series with a very general monotonicity condition in complex sense. A necessary and sufficient condition for the uniform convergence of trigonometric series in the complex space is then established, generalizing a classical theorem of Chaundy and Jolliffe.