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

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 inve...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Gu Caixing, Luo Shuaibing, Xiao Jie
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2017
Materias:	reducing subspace multiplication operator dirichlet space blaschke product local inverse riemann surface 47b35 46e22 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e267cf83995b49aabb2ca8028a78e831
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:e267cf83995b49aabb2ca8028a78e831
record_format	dspace
spelling	oai:doaj.org-article:e267cf83995b49aabb2ca8028a78e8312021-12-02T16:36:59ZReducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces2300-744310.1515/coma-2017-0007https://doaj.org/article/e267cf83995b49aabb2ca8028a78e8312017-02-01T00:00:00Zhttps://doi.org/10.1515/coma-2017-0007https://doaj.org/toc/2300-7443This 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].Gu CaixingLuo ShuaibingXiao JieDe Gruyterarticlereducing subspacemultiplication operatordirichlet spaceblaschke productlocal inverseriemann surface47b3546e22MathematicsQA1-939ENComplex Manifolds, Vol 4, Iss 1, Pp 84-119 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	reducing subspace multiplication operator dirichlet space blaschke product local inverse riemann surface 47b35 46e22 Mathematics QA1-939
spellingShingle	reducing subspace multiplication operator dirichlet space blaschke product local inverse riemann surface 47b35 46e22 Mathematics QA1-939 Gu Caixing Luo Shuaibing Xiao Jie Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
description	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].
format	article
author	Gu Caixing Luo Shuaibing Xiao Jie
author_facet	Gu Caixing Luo Shuaibing Xiao Jie
author_sort	Gu Caixing
title	Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
title_short	Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
title_full	Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
title_fullStr	Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
title_full_unstemmed	Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
title_sort	reducing subspaces for multiplication operators on the dirichlet space through local inverses and riemann surfaces
publisher	De Gruyter
publishDate	2017
url	https://doaj.org/article/e267cf83995b49aabb2ca8028a78e831
work_keys_str_mv	AT gucaixing reducingsubspacesformultiplicationoperatorsonthedirichletspacethroughlocalinversesandriemannsurfaces AT luoshuaibing reducingsubspacesformultiplicationoperatorsonthedirichletspacethroughlocalinversesandriemannsurfaces AT xiaojie reducingsubspacesformultiplicationoperatorsonthedirichletspacethroughlocalinversesandriemannsurfaces
_version_	1718383663379382272

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

Ejemplares similares