Abstract Interpolation in Vector-Valued de Branges–Rovnyak Spaces View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2011-06

AUTHORS

Joseph A. Ball, Vladimir Bolotnikov, Sanne ter Horst

ABSTRACT

Following ideas from the Abstract Interpolation Problem of Katsnelson et al. (Operators in spaces of functions and problems in function theory, vol 146, pp 83–96, Naukova Dumka, Kiev, 1987) for Schur class functions, we study a general metric constrained interpolation problem for functions from a vector-valued de Branges–Rovnyak space associated with an operator-valued Schur class function S. A description of all solutions is obtained in terms of functions from an associated de Branges–Rovnyak space satisfying only a bound on the de Branges–Rovnyak-space norm. Attention is also paid to the case that the map which provides this description is injective. The interpolation problem studied here contains as particular cases (1) the vector-valued version of the interpolation problem with operator argument considered recently in Ball et al. (Proc Am Math Soc 139(2), 609–618, 2011) (for the nondegenerate and scalar-valued case) and (2) a boundary interpolation problem in . In addition, we discuss connections with results on kernels of Toeplitz operators and nearly invariant subspaces of the backward shift operator. More... »

PAGES

227-263

References to SciGraph publications

  • 1990. The Commutant Lifting Approach to Interpolation Problems in NONE
  • 1986. Treatise on the Shift Operator, Spectral Function Theory in NONE
  • 2008-03. Boundary Behavior of Functions in the de Branges–Rovnyak Spaces in COMPLEX ANALYSIS AND OPERATOR THEORY
  • 1986-07. The kernel of a Toeplitz operator in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 1995-09. On a necessary but not sufficient condition for a γ-generating pair to be a nehari pair in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 2008-11. Interpolation Problems for Schur Multipliers on the Drury-Arveson Space: from Nevanlinna-Pick to Abstract Interpolation Problem in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 2008-01. Carathéodory-Julia type theorems for operator valued Schur functions in JOURNAL D'ANALYSE MATHÉMATIQUE
  • 1988. Nearly Invariant Subspaces of the Backward Shift in CONTRIBUTIONS TO OPERATOR THEORY AND ITS APPLICATIONS
  • 2010-05. Kernel of Vector-Valued Toeplitz Operators in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 2008. The Higher Order Carathéodory—Julia Theorem and Related Boundary Interpolation Problems in RECENT ADVANCES IN MATRIX AND OPERATOR THEORY
  • 1997. An abstract interpolation problem and the extension theory of isometric operators in TOPICS IN INTERPOLATION THEORY
  • 1994. An Analysis and Extension of V.P. Potapov’s Approach to Interpolation Problems with Applications to the Generalized Bi-Tangential Schur-Nevanlinna-Pick Problem and J-Inner-Outer Factorization in MATRIX AND OPERATOR VALUED FUNCTIONS
  • 1998-12. On degenerate interpolation, entropy and extremal problems for matrix Schur functions in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00020-010-1844-1

    DOI

    http://dx.doi.org/10.1007/s00020-010-1844-1

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1015032049


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