关于Borel的一个定理(英文)

On A Theorem Of Borel

Borel的一个经典性定理是,如果两组整函数G_i(Z)(i=1,2,…,n)和H_i(Z)(i=1,2,…n)满足恒等式sum from j=1 to n G_i(Z)e^Hj^(Z)≡0 并且如果G_i(1≤i≤n)的增长性,在某种意义下,较慢于e^Hj^(-H)k(1≤j,k≤n,j≠k)的增长性,则G_i(Z)≡0 (i=1,2,…,n),在本文中得出了这个定理的几个推广。

A classical theorem of Borel states that if two systems of entire functions Ci(z) (i = 1, 2, …, n) and Hi(z) (i = 1, 2, …, n) satisfy an identity of the formand if the growth of Gi (1≤i≤n) is, in a certain sense, less rapid than that of eHj-Hk (1≤j, k≤n, j(?)k), then Gi(z)(?)0 (i=1, 2, …, n). In this paper, some extensions of this theorem are obtained.