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The Gohberg Anniversary Collection

Volume II: Topics in Analysis and Operator Theory

  • Book
  • © 1989

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Editors:
  1. H. Dym
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  2. S. Goldberg
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  3. M. A. Kaashoek
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  4. P. Lancaster
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Part of the book series: Operator Theory: Advances and Applications (OT, volume 41)

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Table of contents (29 chapters)

  1. Trigonometric Approximation of Solutions of Periodic Pseudodifferential Equations

    • William McLean, Wolfgang L. Wendland
    Pages 359-383

  2. Wiener-Hopf Factorization of Certain Non-Rational Matrix Functions in Mathematical Physics

    • E. Meister, F.-O. Speck
    Pages 385-394

  3. Classes of Operator Monotone Functions and Stieltjes Functions

    • Yoshihiro Nakamura
    Pages 395-404

  4. A Unified Approach to Function Models, and the Transcription Problem

    • Nikolai K. Nikolskii, Vasily I. Vasyunin
    Pages 405-434

  5. Quadrature Methods for Strongly Elliptic Cauchy Singular Integral Equations on an Interval

    • Siegfried Prössdorf, Andreas Rathsfeld
    Pages 435-471

  6. General Wiener-Hopf Operators and Representation of their Generalized Inverses

    • A. F. dos Santos
    Pages 473-483

  7. Exposed Points in H 1, I

    • Donald Sarason
    Pages 485-496

  8. Geometrical Properties of a Unit Sphere of the Operator Spaces in Lp

    • E. M. Semenov, I. Ya. Shneiberg
    Pages 497-509

  9. C*-Algebras of Crystal Groups

    • Keith F. Taylor
    Pages 511-518

  10. On Wiener-Hopf Determinants

    • Harold Widom
    Pages 519-543

  11. Back Matter

    Pages 545-547
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Keywords

About this book

In this article we shall use two special classes of reproducing kernel Hilbert spaces (which originate in the work of de Branges [dB) and de Branges-Rovnyak [dBRl), respectively) to solve matrix versions of a number of classical interpolation problems. Enroute we shall reinterpret de Branges' characterization of the first of these spaces, when it is finite dimensional, in terms of matrix equations of the Liapunov and Stein type and shall subsequently draw some general conclusions on rational m x m matrix valued functions which are "J unitary" a.e. on either the circle or the line. We shall also make some connections with the notation of displacement rank which has been introduced and extensively studied by Kailath and a number of his colleagues as well as the one used by Heinig and Rost [HR). The first of the two classes of spaces alluded to above is distinguished by a reproducing kernel of the special form K (>.) = J - U(>')JU(w)* (Ll) w Pw(>') , in which J is a constant m x m signature matrix and U is an m x m J inner matrix valued function over ~+, where ~+ is equal to either the open unit disc ID or the open upper half plane (1)+ and Pw(>') is defined in the table below.

Bibliographic Information

  • Book Title: The Gohberg Anniversary Collection

  • Book Subtitle: Volume II: Topics in Analysis and Operator Theory

  • Editors: H. Dym, S. Goldberg, M. A. Kaashoek, P. Lancaster

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-9278-0

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag Basel 1989

  • Hardcover ISBN: 978-3-7643-2308-0Published: 01 July 1989

  • Softcover ISBN: 978-3-0348-9975-8Published: 09 November 2011

  • eBook ISBN: 978-3-0348-9278-0Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: IX, 547

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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