关于超球级数的增长性质

On the Growth of Hyperspherical Series

中文关键词:  整函数  超球级数  极大项  中心指标  正规增长

英文关键词:entire function  hyperspherical series  normal growth.

中文摘要:

      本文给出了超球级数所定义的整函数的极大项μ(a),中心指标υ(a),极大模M(a)的增长关系及它们之间的不等式,还讨论了正规增长性。

英文摘要:

      Let P_n^(a,a) (z) be n-degree hyperspherical holynomials with 0 ≤Reα≤1/2, and f(z)=(?)(z) an entire function. In this paper, some inequalities are found among M(a) =(?)|f(a + bi)| , maximal term μ(a) and central norm v(a) . It is proved that(?).Moreover, a necessary and sufficient condition is given for f(z) = (?) to be regularly growed.