Conservative realizations of Herglotz-Nevanlinna functions

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 theoryin 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 asto 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. Only book covering this spectrum of problems and methods of theHerglotz-Nevanlinna functions realization. First comprehensive coverage of the realization theory for Herglotz-Nevanlinna matrix functions. Contains usefuland important applications. INDICE: 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.

• ISBN: 978-3-7643-9995-5
• Editorial: Springer Basel
• Encuadernacion: Cartoné
• Páginas: 528
• Fecha Publicación: 23/06/2011
• Nº Volúmenes: 1
• Idioma: Inglés