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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Some examples of cyclic vectors in the Dirichlet space


Authors: Leon Brown and William Cohn
Journal: Proc. Amer. Math. Soc. 95 (1985), 42-46
MSC: Primary 30D35; Secondary 30H05, 47B38
DOI: https://doi.org/10.1090/S0002-9939-1985-0796443-9
MathSciNet review: 796443
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Abstract: We consider the Hilbert space of analytic functions in the open unit disc that have a finite Dirichlet integral. For $ 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$, and is cyclic with respect to the shift operator.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0796443-9
Keywords: Hilbert space of analytic functions, Dirichlet integral, cyclic vectors, logarithmic capacity
Article copyright: © Copyright 1985 American Mathematical Society