酉辛群上的一条Tauber型收敛定理

A Tauberian Type Convergent Theorem of Usp ( 2n )

本文给出了如下的酉辛群上的一条Tauber型收敛定理,若u(U)在酉辛群Usp(2n)上连续,且其Fourier系数满足N(f) sum from i,j-1 to N(f) ((C_(ii)~f)~2)=0(1/L^(2n)),则u(U)的Fourier级数的部分和收敛于u(U).

In this paper, we give the proof of the following theorem by the method ofanalysis: If u(U) is continuous in Usp(2n), and its Fourier series coefficents satisfy the f llowing conditionthen the partial summation of the Fourier series of u(U)convergences to u(U).