Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces-Reference-Cited by-同舟云学术

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

Published:2017-02-23 Issue:1 Volume:4 Page:84-119
ISSN:2300-7443
Container-title:Complex Manifolds
language:
Short-container-title:

Author:

Gu Caixing¹,Luo Shuaibing²,Xiao Jie³

Affiliation:

1. 1Department of Mathematics, California Polytechnic State University, San Luis Obispo, CA 93407, United States of America

2. 2College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, China

3. 3Department of Mathematics and Statistics, Memorial University, St. John’s, NL A1C5S7, Canada

Abstract

AbstractThis 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].

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/downloadpdf/journals/coma/4/1/article-p84.xml

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