The necessary and sufficient condition which hyperspherical series on Banach space is entire function is obtained. We also used new method to prove the extended theorem of hyperspherical series. 得出了Banach空间的超球级数为整函数的充分必要条件,并用新方法证明了Banach空间超球级数的展开定理,推广了前人的结果。
In this paper, the type function of zero order and finite positive order of hyperspherical series is investigated. The relationship between its order, maximal module and the type of type function is established. 研究了零阶与有限正阶超球级数的型函数,得出了超球级数的阶、最大模与型函数所对应的型之间的关系式。