单位圆周上广义Fourier积分的收敛性(英文)

CONVERGENCE OF GENERALIZED FOURIER INTEGRAL ON THE UNIT CIRCLE

本文研究了复平面单位圆上的广义Fourier积分.利用经典的Fourier分析的结果和Carleson定理,以及复平面上解析函数在高阶导数下直角坐标和极坐标之间的关系,我们得到了前面定义的广义Fourier积分的一个收敛定理.从而推广了直线上经典Fourier积分的收敛结果.

The present article considers a generalized Fourier integral on the unit circle of complex plane.Based on the classical results of Fourier series and Carleson＇s theorem,and the relationships of high order derivatives between rectangular coordinates and polar coordinates of holomorphic functions in the complex plane,we obtain a convergence theorem of this kind of generalized Fourier integral.Our results generalize the classical results of Fourier integral on the real line.