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

 

Cyclic vectors in the Fock space over the complex plane


Author: Kou Hei Izuchi
Journal: Proc. Amer. Math. Soc. 133 (2005), 3627-3630
MSC (2000): Primary 46J15, 46H25, 47A16
Published electronically: June 3, 2005
MathSciNet review: 2163599
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Abstract: In this paper, we characterize the cyclic vectors in the Fock space over the complex plane. We prove that a function $f(z)$ is cyclic in the Fock space if and only if $f(z)$ is a nonvanishing function in $L^2_a(\mathbb{C})$.


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Additional Information

Kou Hei Izuchi
Affiliation: Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan
Email: f04n010j@mail.cc.niigata-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07938-4
PII: S 0002-9939(05)07938-4
Keywords: Fock space, entire function, cyclic vector
Received by editor(s): July 21, 2004
Received by editor(s) in revised form: August 17, 2004
Published electronically: June 3, 2005
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.