Some examples of cyclic vectors in the Dirichlet space-Reference-Cited by-同舟云学术

Some examples of cyclic vectors in the Dirichlet space

Published:1985 Issue:1 Volume:95 Page:42-46
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Brown Leon,Cohn William

Abstract

We consider the Hilbert space of analytic functions in the open unit disc that have a finite Dirichlet integral. For E E , a closed subset of the unit circle with logarithmic capacity zero, we construct a function in this space which is uniformly continuous, vanishes on E E , and is cyclic with respect to the shift operator.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1985-095-01/S0002-9939-1985-0796443-9/S0002-9939-1985-0796443-9.pdf

Reference4 articles.

1. Cyclic vectors in the Dirichlet space;Brown, Leon;Trans. Amer. Math. Soc.,1984

2. Sets of uniqueness for functions regular in the unit circle;Carleson, Lennart;Acta Math.,1952

3. Van Nostrand Mathematical Studies, No. 13;Carleson, Lennart,1967

4. Actualit\'{e}s Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1301;Kahane, Jean-Pierre,1963

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Cyclicity in de Branges–Rovnyak spaces;Moroccan Journal of Pure and Applied Analysis;2023-05-01

2. The Dirichlet Space;Lectures on Analytic Function Spaces and their Applications;2023

3. Totally null sets and capacity in Dirichlet type spaces;Journal of the London Mathematical Society;2022-04-23

4. Simultaneous zero-free approximation and universal optimal polynomial approximants;Journal of Approximation Theory;2020-08

5. Regularity for generators of invariant subspaces of the Dirichlet shift;Journal of Functional Analysis;2019-10