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

Caixing Gu, Shuaibing Luo, and Jie Xiao. "Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces." Complex Manifolds 4.1 (2017): 84-119. <http://eudml.org/doc/288421>.

@article{CaixingGu2017,
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].},
author = {Caixing Gu, Shuaibing Luo, Jie Xiao},
journal = {Complex Manifolds},
keywords = {Reducing subspace; Multiplication operator; Dirichlet space; Blaschke product; Local inverse; Riemann surface},
language = {eng},
number = {1},
pages = {84-119},
title = {Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces},
url = {http://eudml.org/doc/288421},
volume = {4},
year = {2017},
}

TY - JOUR
AU - Caixing Gu
AU - Shuaibing Luo
AU - Jie Xiao
TI - Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
JO - Complex Manifolds
PY - 2017
VL - 4
IS - 1
SP - 84
EP - 119
AB - 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].
LA - eng
KW - Reducing subspace; Multiplication operator; Dirichlet space; Blaschke product; Local inverse; Riemann surface
UR - http://eudml.org/doc/288421
ER -