The Transformation of Issai Schur and Related Topics in an Indefinite Setting View Full Text


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Chapter Info

DATE

2007

AUTHORS

D. Alpay , A. Dijksma , H. Langer

ABSTRACT

We review our recent work on the Schur transformation for scalar generalized Schur and Nevanlinna functions. The Schur transformation is defined for these classes of functions in several situations, and it is used to solve corresponding basic interpolation problems and problems of factorization of rational J-unitary matrix functions into elementary factors. A key role is played by the theory of reproducing kernel Pontryagin spaces and linear relations in these spaces. More... »

PAGES

1-98

References to SciGraph publications

  • 2003-01. The Schur Algorithm for Generalized Schur Functions II: Jordan Chains and Transformations of Characteristic Functions in MONATSHEFTE FÜR MATHEMATIK
  • 1991-07. Interpolation problems, extensions of symmetric operators and reproducing kernel spaces II in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 2000-03. A factorization result for generalized Nevanlinna functions of the classNk in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 2005. Closely Connected Unitary Realizations of the Solutions to the Basic Interpolation Problem for Generalized Schur Functions in RECENT ADVANCES IN OPERATOR THEORY AND ITS APPLICATIONS
  • 2002-03. J-inner matrix functions, interpolation and inverse problems for canonical systems, IV: Direct and inverse bitangential input scattering problems in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 1984-09. Hilbert spaces of analytic functions, inverse scattering and operator models.I in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 1998-06. Nevanlinna-Pick interpolation with boundary data in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 1907-03. Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen in MATHEMATISCHE ANNALEN
  • 2004-11. Operator-valued Jet Functions with Positive Carathéodory–Pick Operators in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 1911-12. Über die fourier’sche entwickelung positiver funktionen in RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO SERIES 2
  • 1983-12. Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • Book

    TITLE

    System Theory, the Schur Algorithm and Multidimensional Analysis

    ISBN

    978-3-7643-8136-3

    From Grant

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-7643-8137-0_1

    DOI

    http://dx.doi.org/10.1007/978-3-7643-8137-0_1

    DIMENSIONS

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