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Conservative Realizations of Herglotz-Nevanlinna Functions

  • Yuri Arlinskii
  • Sergey Belyi
  • Eduard Tsekanovskii

Part of the Operator Theory: Advances and Applications book series (OT, volume 217)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
    Pages 1-21
  3. Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
    Pages 23-43
  4. Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
    Pages 45-68
  5. Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
    Pages 69-118
  6. Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
    Pages 119-145
  7. Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
    Pages 147-203
  8. Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
    Pages 205-237
  9. Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
    Pages 239-259
  10. Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
    Pages 261-340
  11. Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
    Pages 341-412
  12. Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
    Pages 413-452
  13. Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
    Pages 453-496
  14. Back Matter
    Pages 497-528

About this book

Introduction

This book is devoted to conservative realizations of various classes of Stieltjes, inverse Stieltjes, and general Herglotz-Nevanlinna functions as impedance functions of linear systems. The main feature of the monograph is a new approach to the realization theory profoundly involving developed extension theory in triplets of rigged Hilbert spaces and  unbounded operators as state-space operators of linear systems. The connections of the realization theory to systems with accretive, sectorial, and contractive state-space operators as well as  to the Phillips-Kato sectorial extension problem, the Krein-von Neumann and Friedrichs extremal extensions are provided. Among other results the book contains applications to the inverse problems for linear systems with non-self-adjoint Schrödinger operators,  Jacobi matrices, and to the Nevanlinna-Pick system interpolation.

Keywords

Herglotz-Nevanlinna function operator theory system theory

Authors and affiliations

  • Yuri Arlinskii
    • 1
  • Sergey Belyi
    • 2
  • Eduard Tsekanovskii
    • 3
  1. 1., Department of MathematicsEast Ukrainian National UniversityLuganskUkraine
  2. 2., Department of MathematicsTroy UniversityTroyUSA
  3. 3., Department of MathematicsNiagara UniversityNiagara UniversityUSA

Bibliographic information