Download or read book Conservative Realizations of Herglotz Nevanlinna Functions written by Yuri Arlinskii and published by Springer Science & Business Media. This book was released on 2011-06-21 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Indefinite Inner Product Spaces Schur Analysis and Differential Equations written by Daniel Alpay and published by Birkhäuser. This book was released on 2018-01-30 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book From Complex Analysis to Operator Theory A Panorama written by Malcolm Brown and published by Springer Nature. This book was released on 2023-09-21 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modern Analysis and Applications written by Vadim Adamyan and published by Springer Science & Business Media. This book was released on 2009-08-29 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Recent Advances in Inverse Scattering Schur Analysis and Stochastic Processes written by Daniel Alpay and published by Birkhäuser. This book was released on 2015-04-30 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Operator Methods for Boundary Value Problems written by Seppo Hassi and published by Cambridge University Press. This book was released on 2012-10-11 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Equations Mathematical Physics and Applications Selim Grigorievich Krein Centennial written by Peter Kuchment and published by American Mathematical Soc.. This book was released on 2019-07-22 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 733. Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union. The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in ordinary and partial differential equations, fluid dynamics, and various applications.
Download or read book Introduction to Quantum Graphs written by Gregory Berkolaiko and published by American Mathematical Soc.. This book was released on 2013 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.
Download or read book Large Truncated Toeplitz Matrices Toeplitz Operators and Related Topics written by Dario A. Bini and published by Birkhäuser. This book was released on 2017-03-21 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Unsolved Problems in Mathematical Systems and Control Theory written by Vincent D. Blondel and published by Princeton University Press. This book was released on 2009-04-11 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included here is proposed by a leading expert and set forth in an accessible manner. Covering a wide range of areas, the book will be an ideal reference for anyone interested in the latest developments in the field, including specialists in applied mathematics, engineering, and computer science. The book consists of ten parts representing various problem areas, and each chapter sets forth a different problem presented by a researcher in the particular area and in the same way: description of the problem, motivation and history, available results, and bibliography. It aims not only to encourage work on the included problems but also to suggest new ones and generate fresh research. The reader will be able to submit solutions for possible inclusion on an online version of the book to be updated quarterly on the Princeton University Press website, and thus also be able to access solutions, updated information, and partial solutions as they are developed.
Download or read book Spectral Analysis Differential Equations and Mathematical Physics A Festschrift in Honor of Fritz Gesztesy s 60th Birthday written by Helge Holden and published by American Mathematical Soc.. This book was released on 2013-07-08 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Mathematics Of Open Quantum Systems The Dissipative And Non unitary Representations And Quantum Measurements written by Konstantin A Makarov and published by World Scientific. This book was released on 2021-12-24 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new developments in the open quantum systems theory with emphasis on applications to the (frequent) measurement theory.In the first part of the book, the uniqueness theorems for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions are discussed. The major theme involves an intrinsic characterization of the simplest symmetric operator solutions to the Heisenberg uncertainty relations, the problem posed by Jørgensen and Muhly, followed by the proof of the uniqueness theorems for the simplest solutions to the restricted Weyl commutation relations. The detailed study of unitary invariants of the corresponding dissipative and symmetric operators opens up a look at the classical Stone-von Neumann uniqueness theorem from a new angle and provides an extended version of the uniqueness result relating various realizations of a differentiation operator on the corresponding metric graphs.The second part of the book is devoted to mathematical problems of the quantum measurements under continuous monitoring. Among the topics discussed are the complementarity of the Quantum Zeno effect and Exponential Decay scenario in frequent quantum measurements, and a rigorous treatment, within continuous monitoring paradigm, of the celebrated 'double-slit experiment' where the renowned exclusive and interference measurement alternatives approach in quantum theory is presented in a way that is accessible for mathematicians. One of the striking applications of the generalized (1-stable) central limit theorem is the mathematical evidence of exponential decay of unstable states of the quantum pendulum under continuous monitoring.
Download or read book Concrete Operators Spectral Theory Operators in Harmonic Analysis and Approximation written by Manuel Cepedello Boiso and published by Springer Science & Business Media. This book was released on 2013-11-04 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of research articles and surveys on recent developments on operator theory as well as its applications covered in the IWOTA 2011 conference held at Sevilla University in the summer of 2011. The topics include spectral theory, differential operators, integral operators, composition operators, Toeplitz operators, and more. The book also presents a large number of techniques in operator theory.
Download or read book The Method of Rigged Spaces in Singular Perturbation Theory of Self Adjoint Operators written by Volodymyr Koshmanenko and published by Birkhäuser. This book was released on 2016-07-08 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadratic forms, and the theory of rigged Hilbert spaces. The book will appeal to researchers in mathematics and mathematical physics studying the scales of densely embedded Hilbert spaces, the singular perturbations phenomenon, and singular interaction problems.
Download or read book Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations written by Damir Z. Arov and published by Cambridge University Press. This book was released on 2012-09-13 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essentially self-contained treatment ideal for mathematicians, physicists or engineers whose research is connected with inverse problems.
Download or read book Operator Theory Function Spaces and Applications written by Tanja Eisner and published by Birkhäuser. This book was released on 2016-09-24 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Physics Spectral Theory and Stochastic Analysis written by Michael Demuth and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents self-contained survey articles on modern research areas written by experts in their fields. The topics are located at the interface of spectral theory, theory of partial differential operators, stochastic analysis, and mathematical physics. The articles are accessible to graduate students and researches from other fields of mathematics or physics while also being of value to experts, as they report on the state of the art in the respective fields.
