Beurling’s phenomenon on analytic Hilbert spaces over the complex plane
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Abstract:
In this paper, we show that Beurling’s theorem on analytic Hilbert spaces over the complex plane analogous to the Hardy space or the Bergman space does not hold, but for finite co-dimensional quasi-invariant subspaces, they are generated by their wandering subspace if and only if they are generated by $z^n$ provided that the order of the reproducing kernels $K_\lambda (z)$ is less than 2 but not equal to 1.References
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Additional Information
- Shuyun Wei
- Affiliation: Department of Mathematics, Suzhou University, Jiangsu Suzhou, 215006, People’s Republic of China
- Email: swei@suda.edu.cn
- Received by editor(s): May 6, 2009
- Received by editor(s) in revised form: August 28, 2009
- Published electronically: December 11, 2009
- Additional Notes: The author is partially supported by NNSFC in China, grant No. 10871140
- Communicated by: Nigel J. Kalton
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 1439-1446
- MSC (2010): Primary 46E22, 47A15
- DOI: https://doi.org/10.1090/S0002-9939-09-10196-X
- MathSciNet review: 2578537