Interpolation Problems for Schur Multipliers on the Drury-Arveson Space: from Nevanlinna-Pick to Abstract Interpolation Problem View Full Text


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Article Info

DATE

2008-11

AUTHORS

Joseph A. Ball, Vladimir Bolotnikov

ABSTRACT

We survey various increasingly more general operator-theoretic formulations of generalized left-tangential Nevanlinna-Pick interpolation for Schur multipliers on the Drury-Arveson space. An adaptation of the methods of Potapov and Dym leads to a chain-matrix linear-fractional parametrization for the set of all solutions for all but the last of the formulations for the case where the Pick operator is invertible. The last formulation is a multivariable analogue of the Abstract Interpolation Problem formulated by Katsnelson, Kheifets and Yuditskii for the single-variable case; we obtain a Redheffer-type linear-fractional parametrization for the set of all solutions (including in degenerate cases) via an adaptation of ideas of Arov and Grossman. More... »

PAGES

301-349

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00020-008-1626-1

DOI

http://dx.doi.org/10.1007/s00020-008-1626-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1022973028


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