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Beurling's phenomenon on analytic Hilbert spaces over the complex plane

Author: Shuyun Wei
Journal: Proc. Amer. Math. Soc. 138 (2010), 1439-1446
MSC (2010): Primary 46E22, 47A15
Published electronically: December 11, 2009
MathSciNet review: 2578537
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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.

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Additional Information

Shuyun Wei
Affiliation: Department of Mathematics, Suzhou University, Jiangsu Suzhou, 215006, People’s Republic of China

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
Article copyright: © Copyright 2009 American Mathematical Society

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