关于超球级数的增长性质

On the Growth of Hyperspherical Series

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。

Let Pn(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) = max |f(a + bi)| , maximal term μ(a) and central norm v(a) . It is proved that liminf limsup Moreover, a necessary and sufficient condition is given for f(z) = (z) to be regularly growed.