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Conservative Realizations of Herglotz-Nevanlinna Functions

Author: Yuri Arlinskii

Publisher: Springer Science & Business Media

Published: 2011-06-21

Total Pages: 540

ISBN-13: 3764399961

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.

Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations

Author: Daniel Alpay

Publisher: Birkhäuser

Published: 2018-01-30

Total Pages: 495

ISBN-13: 3319688499

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This volume, which is dedicated to Heinz Langer, includes biographical material and carefully selected papers. Heinz Langer has made fundamental contributions to operator theory. In particular, he has studied the domains of operator pencils and nonlinear eigenvalue problems, the theory of indefinite inner product spaces, operator theory in Pontryagin and Krein spaces, and applications to mathematical physics. His works include studies on and applications of Schur analysis in the indefinite setting, where the factorization theorems put forward by Krein and Langer for generalized Schur functions, and by Dijksma-Langer-Luger-Shondin, play a key role. The contributions in this volume reflect Heinz Langer’s chief research interests and will appeal to a broad readership whose work involves operator theory.

From Complex Analysis to Operator Theory: A Panorama

Author: Malcolm Brown

Publisher: Springer Nature

Published: 2023-09-21

Total Pages: 731

ISBN-13: 3031311396

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This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.

Modern Analysis and Applications

Author: Vadim Adamyan

Publisher: Springer Science & Business Media

Published: 2009-08-29

Total Pages: 497

ISBN-13: 3764399198

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This is the first of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.

Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics

Author: Dario A. Bini

Publisher: Birkhäuser

Published: 2017-03-21

Total Pages: 757

ISBN-13: 3319491822

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This book presents a collection of expository and research papers on various topics in matrix and operator theory, contributed by several experts on the occasion of Albrecht Böttcher’s 60th birthday. Albrecht Böttcher himself has made substantial contributions to the subject in the past. The book also includes a biographical essay, a complete bibliography of Albrecht Böttcher’s work and brief informal notes on personal encounters with him. The book is of interest to graduate and advanced undergraduate students majoring in mathematics, researchers in matrix and operator theory as well as engineers and applied mathematicians.

Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

Author: Damir Z. Arov

Publisher: Cambridge University Press

Published: 2012-09-13

Total Pages: 487

ISBN-13: 1107018870

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An essentially self-contained treatment ideal for mathematicians, physicists or engineers whose research is connected with inverse problems.

Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes

Author: Daniel Alpay

Publisher: Birkhäuser

Published: 2015-04-30

Total Pages: 396

ISBN-13: 3319103350

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The volume is dedicated to Lev Sakhnovich, who made fundamental contributions in operator theory and related topics. Besides bibliographic material, it includes a number of selected papers related to Lev Sakhnovich's research interests. The papers are related to operator identities, moment problems, random matrices and linear stochastic systems.

Operator Theory, Function Spaces, and Applications

Author: Tanja Eisner

Publisher: Birkhäuser

Published: 2016-09-24

Total Pages: 240

ISBN-13: 3319313835

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This volume collects a selected number of papers presented at the International Workshop on Operator Theory and its Applications (IWOTA) held in July 2014 at Vrije Universiteit in Amsterdam. Main developments in the broad area of operator theory are covered, with special emphasis on applications to science and engineering. The volume also presents papers dedicated to the eightieth birthday of Damir Arov and to the sixty-fifth birthday of Leiba Rodman, both leading figures in the area of operator theory and its applications, in particular, to systems theory.

Operator Methods for Boundary Value Problems

Author: Seppo Hassi

Publisher: Cambridge University Press

Published: 2012-10-11

Total Pages: 297

ISBN-13: 1139561316

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Presented in this volume are a number of new results concerning the extension theory and spectral theory of unbounded operators using the recent notions of boundary triplets and boundary relations. This approach relies on linear single-valued and multi-valued maps, isometric in a Krein space sense, and offers a basic framework for recent developments in system theory. Central to the theory are analytic tools such as Weyl functions, including Titchmarsh-Weyl m-functions and Dirichlet-to-Neumann maps. A wide range of topics is considered in this context from the abstract to the applied, including boundary value problems for ordinary and partial differential equations; infinite-dimensional perturbations; local point-interactions; boundary and passive control state/signal systems; extension theory of accretive, sectorial and symmetric operators; and Calkin's abstract boundary conditions. This accessible treatment of recent developments, written by leading researchers, will appeal to a broad range of researchers, students and professionals.

Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday

Author: Helge Holden

Publisher: American Mathematical Soc.

Published: 2013-07-08

Total Pages: 409

ISBN-13: 0821875744

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This volume contains twenty contributions in the area of mathematical physics where Fritz Gesztesy made profound contributions. There are three survey papers in spectral theory, differential equations, and mathematical physics, which highlight, in particu