Conservative Realizations of Herglotz-Nevanlinna Functions

• Main Authors: Arlinskii, Yuri (Author), Belyi, Sergey (Author), Tsekanovskii, Eduard (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel, 2011.
• Series: Operator Theory: Advances and Applications ; 217
• Subjects: Mathematics.; Operator theory.; Physics.; Operator Theory.; Mathematical Methods in Physics.

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 exten...

Table of Contents:

• Preface
• 1 Extensions of Symmetric Operators
• 2 Rigged Hilbert Spaces
• 3 Bi-extensions of Closed Symmetric Operators.-.4 Quasi-self-adjoint Extensions
• 5 The Livsic Canonical Systems with Bounded Operators
• 6 Herglotz-Nevanlinna functions and Rigged Canonical Systems
• 7 Classes of realizable Herglotz-Nevanlinna functions
• 8 Normalized Canonical Systems
• 9 Canonical L-systems with Contractive and Accretive Operators
• 10 Systems with Schrödinger operator
• 11 Non-self-adjoint Jacobi Matrices and System Interpolation
• 12 Non-canonical Systems
• Notes and Comments
• References
• Index.