【作者】 刘雨；

【导师】 卢玉峰；

【作者基本信息】 大连理工大学 ， 基础数学， 2019， 硕士

【摘要】 对于单变量的经典Hardy空间,我们由Beurling定理可以清楚的得到不变子空间的形式.但是对于双圆盘的Hardy空间情况就比较复杂,于是可以先从一些相对简单的具体子模入手,从而对一般的情形有更好的理解.本文主要研究了两类特殊的子模:内序列基子模M=(?)∞j=0qjH2(z)ωj和双内序列基子模M=∑∞j=0φj(z)H2(z)(?)(Ψj(ω)H2(ω)(?)Ψj+1(ω)H2(ω)).研究它们对应的商子模在什么样的条件下有不变分解.更多还原

【Abstract】 For the classical Hardy space with one variable,we can get the form of invariant subspace by the Beurling theorem.But for the bidisk of the Hardy space is more complex,so we can start with some relatively simple concrete submodules,so as to have a better understanding of the general situation.In this paper,we study two special submodules:inner sequence based invariant submodule M=(?)∞j=0 qjH2(z)ωj and two inner sequences based invariant submodule M=∑∞j=0φj(z)H2(z)(?)(Ψj(ω)H2(ω)(?)Ψj+1(w)H2(ω)).We study that under what conditions do their corresponding quotient submodules have invariant decomposition.更多还原