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A Beurling-type theorem for the Fock space


Authors: Xiaoman Chen and Shengzhao Hou
Journal: Proc. Amer. Math. Soc. 131 (2003), 2791-2795
MSC (2000): Primary 46J15, 46H25, 47A15
DOI: https://doi.org/10.1090/S0002-9939-03-06803-5
Published electronically: January 8, 2003
MathSciNet review: 1974336
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Abstract: Let $M$ be a finite codimensional quasi-invariant subspace of the Fock space $L^2_a({\mathbb C})$. Then there exists a polynomial $q$ such that $M=[q]$. We show that $[q]\ominus [zq]$generates $M$ if and only if $q=z^n$ for some $n\geq 0$.


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Additional Information

Xiaoman Chen
Affiliation: Institute of Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China
Email: xchen@fudan.edu.cn

Shengzhao Hou
Affiliation: Department of Mathematics, Shanxi Teachers University, Linfen, 041004, People’s Republic of China
Address at time of publication: Institute of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China
Email: szhou@etang.com

DOI: https://doi.org/10.1090/S0002-9939-03-06803-5
Received by editor(s): November 6, 2001
Received by editor(s) in revised form: April 2, 2002
Published electronically: January 8, 2003
Additional Notes: This work was supported by NSFC, Lab Math. for Nonlinear Sciences at Fudan Univ., Fund of Shanxi Province for young people
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society