M_(φ)-type Submodules over the Bidisk  

作　　者：Guo Zeng YANG Chang Hui WU Tao YU 

机构地区：[1]School of Mathematics and Statistics,Zhengzhou Normal University,Zhengzhou 450044,P.R.China [2]School of Mathematical Sciences,Qufu Normal University,Qufu 273165,P.R.China [3]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第5期805-824,共20页数学学报（英文版）

基　　金：Supported by NNSF of China(Grant No.11971087)。

摘　　要：Let H^(2)(D^(2))be the Hardy space over the bidisk D^(2),and let M_(φ)=[(z-φ(w))^(2)]be the submodule generated by(z-φ(w))^(2),whereφ(w)is a function in H∞(w).The related quotient module is denoted by N_(φ)=H^(2)(D^(2))ΘM_(φ).In the present paper,we study the Fredholmness of compression operators S_(z),S_(w) on N_(φ).Whenφ(w)is a nonconstant inner function,we prove that the Beurling type theorem holds for the fringe operator F_(w) on[(z-w)^(2)]Θz[(z-w)^(2)]and the Beurling type theorem holds for the fringe operator Fz on M_(φ)ΘwM_(φ)ifφ(0)=0.Lastly,we study some properties of F_(w) on[(z-w^(2))^(2)]Θz[(z-w^(2))^(2)].

关 键 词：Submodules Beurling type theorem compression operators FREDHOLMNESS 

分 类 号：O177[理学—数学]