M-phi-type Submodules over the Bidisk
发布时间：2021-07-04
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- 论文类型：
- 期刊论文
- 发表时间：
- 2021-06-05
- 发表刊物：
- ACTA MATHEMATICA SINICA-ENGLISH SERIES
- 文献类型：
- J
- 卷号：
- 37
- 期号：
- 5
- 页面范围：
- 805-824
- ISSN号：
- 1439-8516
- 关键字：
- Submodules; Beurling type theorem; compression operators; Fredholmness
- 摘要：
- Let H-2(D-2) be the Hardy space over the bidisk D-2, and let M-phi = [(z - phi(w))(2)] be the submodule generated by (z - phi(w))(2), where phi(w) is a function in H-infinity(w). The related quotient module is denoted by N phi=H-2(D-2)circle minus M phi. In the present paper, we study the Fredholmness of compression operators S-z, S-w on N-phi. When phi(w) is a nonconstant inner function, we prove that the Beurling type theorem holds for the fringe operator F-w on [(z - w)(2)] circle minus z[(z - w)(2)] and the Beurling type theorem holds for the fringe operator F-z on M-phi circle minus wM(phi) if phi(0) = 0. Lastly, we study some properties of F-w on [(z - w(2))(2)] circle minus z[(z - w(2))(2)].
- 第一作者
- Yang, Guo Zeng
- 通讯作者
- Wu, Chang Hui,于涛