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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Interpolation for multipliers on reproducing kernel Hilbert spaces


Author: Vladimir Bolotnikov
Journal: Proc. Amer. Math. Soc. 131 (2003), 1373-1383
MSC (2000): Primary 41A05, 46E22
Published electronically: December 6, 2002
MathSciNet review: 1949867
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Abstract: All solutions of a tangential interpolation problem for contractive multipliers between two reproducing kernel Hilbert spaces of analytic vector-valued functions are characterized in terms of certain positive kernels. In a special important case when the spaces consist of analytic functions on the unit ball of $\mathbb{C} ^d$ and the reproducing kernels are of the form $(1-\langle z,w\rangle^{-1})I_p$ and $(1-\langle z,w\rangle)^{-1}I_q$, the characterization leads to a parametrization of the set of all solutions in terms of a linear fractional transformation.


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Additional Information

Vladimir Bolotnikov
Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187-8795
Email: vladi@math.wm.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06899-5
PII: S 0002-9939(02)06899-5
Received by editor(s): February 24, 2001
Received by editor(s) in revised form: March 23, 2001
Published electronically: December 6, 2002
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society