A Beurling-type theorem for the Fock space
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- by Xiaoman Chen and Shengzhao Hou PDF
- Proc. Amer. Math. Soc. 131 (2003), 2791-2795 Request permission
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 $n\geq 0$.References
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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
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 1974336