$\ell^{p}_{A}$的内函数和零集
Inner functions and zero sets for $\ell^{p}_{A}$
摘要：
在本文中，我们从$\ell^{p}_{A}$（开单位圆盘$D$上的解析函数，其泰勒系数形成$\ell^p$序列）的零集的功能的特点，通过发展的概念，一个“内函数”的希尔伯特空间$\ell^{2}_{A}$（经典的哈代空间）的讨论建模。零集准则用于构造经典结果中未包含的零集族。特别地，证明了当$p > 2$时，存在非Blaschke序列的$\ell^{p}_{A}$的零集.
英文摘要：
In this paper we characterize the zero sets of functions from $\ell^{p}_{A}$ (the analytic functions on the open unit disk $D$ whose Taylor coefficients form an $\ell^p$ sequence) by developing a concept of an "inner function" modeled by Beurling's discussion of the Hilbert space $\ell^{2}_{A}$ (the classical Hardy space). The zero set criterion is used to construct families of zero sets which are not covered by classical results. In particular, it is proved that when $p > 2$, there are zero sets for $\ell^{p}_{A}$ which are not Blaschke sequences.
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