Cyclic vectors in the Fock space over the complex plane
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- by Kou Hei Izuchi PDF
- Proc. Amer. Math. Soc. 133 (2005), 3627-3630 Request permission
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 $L^2_a(\mathbb {C})$.References
- Carlos A. Berenstein and Roger Gay, Complex variables, Graduate Texts in Mathematics, vol. 125, Springer-Verlag, New York, 1991. An introduction. MR 1107514, DOI 10.1007/978-1-4612-3024-3
- Xiaoman Chen and Kunyu Guo, Analytic Hilbert modules, Chapman & Hall/CRC Research Notes in Mathematics, vol. 433, Chapman & Hall/CRC, Boca Raton, FL, 2003. MR 1988884, DOI 10.1201/9780203008836
- Xiaoman Chen, Kunyu Guo, and Shengzhao Hou, Analytic Hilbert spaces over the complex plane, J. Math. Anal. Appl. 268 (2002), no. 2, 684–700. MR 1896222, DOI 10.1006/jmaa.2001.7839
- Xiaoman Chen and Shengzhao Hou, A Beurling-type theorem for the Fock space, Proc. Amer. Math. Soc. 131 (2003), no. 9, 2791–2795. MR 1974336, DOI 10.1090/S0002-9939-03-06803-5
- John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
- Kunyu Guo and Dechao Zheng, Invariant subspaces, quasi-invariant subspaces, and Hankel operators, J. Funct. Anal. 187 (2001), no. 2, 308–342. MR 1875150, DOI 10.1006/jfan.2001.3820
- Haakan Hedenmalm, Boris Korenblum, and Kehe Zhu, Theory of Bergman spaces, Graduate Texts in Mathematics, vol. 199, Springer-Verlag, New York, 2000. MR 1758653, DOI 10.1007/978-1-4612-0497-8
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- Walter Rudin, Real and complex analysis, 3rd ed., McGraw-Hill Book Co., New York, 1987. MR 924157
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
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3627-3630
- MSC (2000): Primary 46J15, 46H25, 47A16
- DOI: https://doi.org/10.1090/S0002-9939-05-07938-4
- MathSciNet review: 2163599