Table of contents

  1. Front Matter
    Pages i-xix
  2. Reproducing Kernel Hilbert Spaces

    1. Front Matter
      Pages 1-1
    2. Franciszek Hugon Szafraniec
      Pages 3-30
    3. Łukasz Kosiński, Włodzimierz Zwonek
      Pages 73-86
    4. Daniel Beltiţǎ, José E. Galé
      Pages 127-148
  3. Indefinite Inner Product Spaces

  4. de Branges Spaces

    1. Front Matter
      Pages 471-472
    2. Harald Woracek
      Pages 489-523
    3. Henrik Winkler
      Pages 525-547
    4. Luis O. Silva, Julio H. Toloza
      Pages 549-580
    5. Roman Romanov
      Pages 609-621
    6. Christian Remling
      Pages 623-630
    7. Joseph A. Ball, Vladimir Bolotnikov
      Pages 631-679
    8. Joseph A. Ball, Vladimir Bolotnikov
      Pages 681-720
    9. Damir Z. Arov, Harry Dym
      Pages 721-752
    10. Damir Z. Arov, Harry Dym
      Pages 753-776
  5. Linear Systems Theory

    1. Front Matter
      Pages 777-777
    2. Yury Arlinskiı̆, Sergey Belyi, Eduard Tsekanovskiı̆
      Pages 779-809
    3. Patrick Dewilde, Alle-Jan Van der Veen
      Pages 901-930
    4. Phillip A. Regalia
      Pages 931-966
  6. Multivariable Operator Theory

    1. Front Matter
      Pages 967-968
    2. Caline Ambrozie, Vladimír Müller
      Pages 1093-1124
    3. Vladimír Müller
      Pages 1181-1215
  7. Infinite Dimensional Analysis

    1. Front Matter
      Pages 1217-1219
    2. Palle E. T. Jorgensen, Feng Tian
      Pages 1221-1243

About this book


A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.


Schur analysis de Branges spaces indefinite inner product spaces infinite dimensional analysis noncommutative analysis reproducing kernel Hilbert spaces

Editors and affiliations

  • Daniel Alpay
    • 1
  1. 1.Earl Katz Chair in Algebraic System Theory, Department of MathematicsBen-Gurion University of the NegevBe’er ShevaIsrael

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