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Interpolation in de Branges-Rovnyak spaces

Authors: Joseph A. Ball, Vladimir Bolotnikov and Sanne ter Horst
Journal: Proc. Amer. Math. Soc. 139 (2011), 609-618
MSC (2010): Primary 30E05, 47A57, 46E22
Published electronically: July 1, 2010
MathSciNet review: 2736342
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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.

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Additional Information

Joseph A. Ball
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123

Vladimir Bolotnikov
Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187-8795

Sanne ter Horst
Affiliation: Mathematical Institute, Utrecht University, P.O. Box 80 010, 3508 TA Utrecht, The Netherlands

Keywords: de Branges-Rovnyak space, Schur-class function
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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