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Interpolation and Realization Theory with Applications to Control Theory

In Honor of Joe Ball

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  • © 2019

Overview

Editors:
  1. Vladimir Bolotnikov

    1. Department of Mathematics, The College of William and Mary, Williamsburg, USA

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  2. Sanne ter Horst

    1. Department of Mathematics, Unit for BMI, North-West University, Potchefstroom, South Africa

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  3. André C.M. Ran

    1. Department of Mathematics, Faculty of Science, VU Amsterdam, Amsterdam, The Netherlands

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  4. Victor Vinnikov

    1. Department of Mathematics, Ben Gurion University of the Negev, Be’er-Sheva, Israel

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  • Includes fourteen original research papers by friends and colleagues of Joe Ball
  • Honors the mathematical life of Joe Ball
  • Presents latest results in the fields of operator theory

Part of the book series: Operator Theory: Advances and Applications (OT, volume 272)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xli
    Download chapter PDF

  2. Holomorphic Operator-valued Functions Generated by Passive Selfadjoint Systems

    • Yuri Arlinskiĭ, Seppo Hassi
    Pages 1-42

  3. Free Bianalytic Maps between Spectrahedra and Spectraballs in a Generic Setting

    • Meric Augat, J. William Helton, Igor Klep, Scott McCullough
    Pages 43-60

  4. Szegő and Widom Theorems for the Neil Algebra

    • Sriram Balasubramanian, Scott McCullough, Udeni Wijesooriya
    Pages 61-70

  5. Block Triangular Matrices in Banach Space: Minimal Completions and Factorability

    • Nir Cohen
    Pages 71-98

  6. Multipliers of Drury–Arveson Space: A Survey

    • Quanlei Fang
    Pages 99-116

  7. Contractively Embedded Invariant Subspaces

    • Sushil Gorai, Jaydeb Sarkar
    Pages 117-131

  8. A Toeplitz-like Operator with Rational Symbol Having Poles on the Unit Circle II: The Spectrum

    • G. J. Groenewald, S. ter Horst, J. Jaftha, A. C. M. Ran
    Pages 133-154

  9. The Twofold Ellis–Gohberg Inverse Problem in an Abstract Setting and Applications

    • S. ter Horst, M. A. Kaashoek, F. van Schagen
    Pages 155-212

  10. Abstract Interpolation Problem and Some Applications. II: Coefficient Matrices

    • A. Kheifets
    Pages 213-234

  11. Analytic Interpolation into the Tetrablock and a μ-synthesis Problem

    • Zinaida A. Lykova, N. J. Young, Amos E. Ajibo
    Pages 235-247

  12. A Gleason Solution Model for Row Contractions

    • Robert T. W. Martin, Andriamanankasina Ramanantoanina
    Pages 249-305

  13. On the Augmented Biot-JKD Equations with Pole-Residue Representation of the Dynamic Tortuosity

    • Miao-Jung Yvonne Ou, Hugo J. Woerdeman
    Pages 307-328

  14. The Flow Equations of Resistive Electrical Networks

    • Arjan van der Schaft
    Pages 329-341

  15. Control and the Analysis of Cancer Growth Models

    • Allen Tannenbaum, Tryphon T. Georgiou, Joseph O. Deasy, Larry Norton
    Pages 343-353
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Keywords

About this book

This volume is devoted to Joseph A. (Joe) Ball’s contributions to operator theory and its applications and in celebration of his seventieth birthday.

Joe Ball’s career spans over four and a half decades, starting with his work on model theory and related topics for non-contractions and operators on multiply connected domains. Later on, more applied operator theory themes appeared in his work, involving factorization and interpolation for operator-valued functions, with extensive applications in system and control theory. He has worked on nonlinear control, time-varying systems and, more recently, on multidimensional systems and noncommutative H∞-theory on the unit ball and polydisk, and more general domains, and these are only the main themes in his vast oeuvre.

Fourteen research papers constitute the core of this volume, written by mathematicians who have collaborated with Joe or have been influenced by his vast mathematical work. A curriculum vitae, a publicationslist and a list of Joe Ball’s PhD students are included in this volume, as well as personal reminiscences by colleagues and friends.

Contributions by Yu. M. Arlinskii, S. Hassi, M. Augat, J. W. Helton, I. Klep, S. McCullough, S. Balasubramanian, U. Wijesooriya, N. Cohen, Q. Fang, S. Gorai, J. Sarkar, G. J. Groenewald, S. ter Horst, J. Jaftha, A. C. M. Ran, M.A. Kaashoek, F. van Schagen, A. Kheifets, Z. A. Lykova, N. J. Young, A. E. Ajibo, R. T. W. Martin, A. Ramanantoanina, M.-J. Y. Ou, H. J. Woerdeman, A. van der Schaft, A. Tannenbaum, T. T. Georgiou, J. O. Deasy and L. Norton.




Editors and Affiliations

  • Department of Mathematics, The College of William and Mary, Williamsburg, USA

    Vladimir Bolotnikov

  • Department of Mathematics, Unit for BMI, North-West University, Potchefstroom, South Africa

    Sanne ter Horst

  • Department of Mathematics, Faculty of Science, VU Amsterdam, Amsterdam, The Netherlands

    André C.M. Ran

  • Department of Mathematics, Ben Gurion University of the Negev, Be’er-Sheva, Israel

    Victor Vinnikov

Bibliographic Information

  • Book Title: Interpolation and Realization Theory with Applications to Control Theory

  • Book Subtitle: In Honor of Joe Ball

  • Editors: Vladimir Bolotnikov, Sanne ter Horst, André C.M. Ran, Victor Vinnikov

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-030-11614-9

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-11613-2Published: 17 April 2019

  • eBook ISBN: 978-3-030-11614-9Published: 08 April 2019

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XLI, 353

  • Number of Illustrations: 29 illustrations in colour

  • Topics: Operator Theory

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