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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hypercyclic property of weighted composition operators


Authors: B. Yousefi and H. Rezaei
Journal: Proc. Amer. Math. Soc. 135 (2007), 3263-3271
MSC (2000): Primary 47B33, 47B38
Published electronically: May 14, 2007
MathSciNet review: 2322758
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Abstract: In the present paper we investigate conditions under which a holomorphic self-map of the open unit disk induces a hypercyclic weighted composition operator in the space of holomorphic functions.


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Additional Information

B. Yousefi
Affiliation: Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran
Email: byousefi@shirazu.ac.ir

H. Rezaei
Affiliation: Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08833-8
PII: S 0002-9939(07)08833-8
Keywords: Weighted composition operator, hypercyclic operator, Denjoy-Wolff point, Julia-Carath\'eodory theorem, linear-fractional model theorem, Schwarz's lemma.
Received by editor(s): January 26, 2006
Received by editor(s) in revised form: June 30, 2006
Published electronically: May 14, 2007
Additional Notes: This paper is a part of the second author’s doctoral thesis written at Shiraz University under the direction of the first author
Dedicated: Dedicated to the memory of Professor K. Seddighi
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.