The backward shift on Dirichlet-type spaces
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- by Stephan Ramon Garcia PDF
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Abstract:
We study the backward shift operator on Hilbert spaces ${\mathcal {H}}_{\alpha }$ (for ${\alpha \geq 0}$) which are norm equivalent to the Dirichlet-type spaces $D_{\alpha }$. Although these operators are unitarily equivalent to the adjoints of the forward shift operator on certain weighted Bergman spaces, our approach is direct and completely independent of the standard Cauchy duality. We employ only the classical Hardy space theory and an elementary formula expressing the inner product on ${\mathcal {H}}_{\alpha }$ in terms of a weighted superposition of backward shifts.References
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Additional Information
- Stephan Ramon Garcia
- Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California, 93106-3080
- MR Author ID: 726101
- Email: garcias@math.ucsb.edu
- Received by editor(s): May 8, 2004
- Received by editor(s) in revised form: May 31, 2004
- Published electronically: March 31, 2005
- Communicated by: Joseph A. Ball
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3047-3056
- MSC (2000): Primary 30D55, 47B38
- DOI: https://doi.org/10.1090/S0002-9939-05-07852-4
- MathSciNet review: 2159784