关于Banach空间中超球级数的两个定理

On two theorems of hyperspherical series on Banach space

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。

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.