Interpolation in de Branges-Rovnyak spaces
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- by Joseph A. Ball, Vladimir Bolotnikov and Sanne ter Horst PDF
- Proc. Amer. Math. Soc. 139 (2011), 609-618 Request permission
Abstract:
A general interpolation problem with operator argument is studied for functions $f$ from the de Branges-Rovnyak space $\mathcal {H}(K_s)$ associated with an analytic function $s$ mapping the open unit disk $\mathbb D$ into the closed unit disk. The interpolation condition is taken in the Rosenblum-Rovnyak form $f(A)c=b$ (with a suitable interpretation of $f(A)c$) for given Hilbert space operator $A$ and two vectors $b,c$ from the same space.References
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Additional Information
- Joseph A. Ball
- Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
- MR Author ID: 30070
- Vladimir Bolotnikov
- Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187-8795
- MR Author ID: 266846
- Sanne ter Horst
- Affiliation: Mathematical Institute, Utrecht University, P.O. Box 80 010, 3508 TA Utrecht, The Netherlands
- Received by editor(s): November 13, 2009
- Received by editor(s) in revised form: March 14, 2010
- Published electronically: July 1, 2010
- Additional Notes: The second author was supported by National Science Foundation Grant DMS 0901124
- Communicated by: Nigel J. Kalton
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 609-618
- MSC (2010): Primary 30E05, 47A57, 46E22
- DOI: https://doi.org/10.1090/S0002-9939-2010-10505-1
- MathSciNet review: 2736342