Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2017-02-23 DOI:10.1515/coma-2017-0007

Caixing Gu, S. Luo, J. Xiao

引用次数: 4

Abstract

Abstract This paper gives a full characterization of the reducing subspaces for the multiplication operator Mϕ on the Dirichlet space with symbol of finite Blaschke product ϕ of order 5I 6I 7. The reducing subspaces of Mϕ on the Dirichlet space and Bergman space are related. Our strategy is to use local inverses and Riemann surfaces to study the reducing subspaces of Mϕ on the Bergman space. By this means, we determine the reducing subspaces of Mϕ on the Dirichlet space and answer some questions of Douglas-Putinar-Wang in [6].

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通过局部逆和Riemann曲面减少Dirichlet空间上乘法算子的子空间

摘要本文给出了Dirichlet空间上具有5I6I7阶有限Blaschke乘积的符号的乘法算子M。M在Dirichlet空间和Bergman空间上的约化子空间是相关的。我们的策略是使用局部逆和黎曼曲面来研究Bergman空间上M的归约子空间。通过这种方法，我们确定了M在Dirichlet空间上的约化子空间，并回答了Douglas Putinar Wang在[6]中的一些问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.