A Beurling-type theorem for the Fock space
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- by Xiaoman Chen and Shengzhao Hou
- Proc. Amer. Math. Soc. 131 (2003), 2791-2795
- DOI: https://doi.org/10.1090/S0002-9939-03-06803-5
- Published electronically: January 8, 2003
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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 $n\geq 0$.References
- A. Aleman, S. Richter, and C. Sundberg, Beurling’s theorem for the Bergman space, Acta Math. 177 (1996), no. 2, 275–310. MR 1440934, DOI 10.1007/BF02392623
- W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Wiley 7th edition 2001.
- Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
- J. Conway, Functions of one complex variable, Springer-Verlag, GTM 11 (1978).
- X. Chen, G. Guo and S. Hou, Analytic Hilbert spaces over the Complex plane $\mathbb C$, to appear in JMAA.
- I. Daubechies and A. Grossmann, Frames in the Bargman space of entire functions, Comm. Pure Appl. Math., 41 (1988) 661-680.
- Kunyu Guo, Characteristic spaces and rigidity for analytic Hilbert modules, J. Funct. Anal. 163 (1999), no. 1, 133–151. MR 1682835, DOI 10.1006/jfan.1998.3380
- Kunyu Guo, Algebraic reduction for Hardy submodules over polydisk algebras, J. Operator Theory 41 (1999), no. 1, 127–138. MR 1675180
- Kunyu Guo, Equivalence of Hardy submodules generated by polynomials, J. Funct. Anal. 178 (2000), no. 2, 343–371. MR 1802898, DOI 10.1006/jfan.2000.3659
- K. Guo, The codimension formula on AF-cosubmodules, to appear in Chin. Ann. of Math.
- K. Guo and D. Zheng, Invariant subspaces, quasi-invariant subspaces and Hankel operators, J. Funct. Anal. 187(2001), 308-342.
- Per Jan Håkan Hedenmalm, An invariant subspace of the Bergman space having the codimension two property, J. Reine Angew. Math. 443 (1993), 1–9. MR 1241125, DOI 10.1515/crll.1993.443.1
- Håkan Hedenmalm and Ke He Zhu, On the failure of optimal factorization for certain weighted Bergman spaces, Complex Variables Theory Appl. 19 (1992), no. 3, 165–176. MR 1284108, DOI 10.1080/17476939208814569
- Stefan Richter, Invariant subspaces of the Dirichlet shift, J. Reine Angew. Math. 386 (1988), 205–220. MR 936999, DOI 10.1515/crll.1988.386.205
Bibliographic 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