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Author : William Wilbur Johnston
Publisher :
ISBN 13 :
Total Pages : 198 pages
Book Rating : 4.X/5 (1 download)
Download or read book Spectral Theory for Perturbed Toeplitz Operators written by William Wilbur Johnston and published by . This book was released on 1988 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ronald G. Douglas
Publisher : American Mathematical Soc.
ISBN 13 : 9780821888643
Total Pages : 66 pages
Book Rating : 4.8/5 (886 download)
Download or read book Banach Algebra Techniques in the Theory of Toeplitz Operators written by Ronald G. Douglas and published by American Mathematical Soc.. This book was released on 1980 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Albrecht Boettcher
Publisher : SIAM
ISBN 13 : 9780898717853
Total Pages : 421 pages
Book Rating : 4.7/5 (178 download)
Download or read book Spectral Properties of Banded Toeplitz Matrices written by Albrecht Boettcher and published by SIAM. This book was released on 2005-01-01 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained introduction to the behavior of several spectral characteristics of large Toeplitz band matrices is the first systematic presentation of a relatively large body of knowledge. Covering everything from classic results to the most recent developments, Spectral Properties of Banded Toeplitz Matrices is an important resource. The spectral characteristics include determinants, eigenvalues and eigenvectors, pseudospectra and pseudomodes, singular values, norms, and condition numbers. Toeplitz matrices emerge in many applications and the literature on them is immense. They remain an active field of research with many facets, and the material on banded ones until now has primarily been found in research papers.
Author : Roland Hagen
Publisher : Birkhäuser
ISBN 13 : 3034890672
Total Pages : 388 pages
Book Rating : 4.0/5 (348 download)
Download or read book Spectral Theory of Approximation Methods for Convolution Equations written by Roland Hagen and published by Birkhäuser. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present book is to propose a new algebraic approach to the study of norm stability of operator sequences which arise, for example, via discretization of singular integral equations on composed curves. A wide variety of discretization methods, including quadrature rules and spline or wavelet approximations, is covered and studied from a unique point of view. The approach takes advantage of the fruitful interplay between approximation theory, concrete operator theory, and local Banach algebra techniques. The book is addressed to a wide audience, in particular to mathematicians working in operator theory and Banach algebras as well as to applied mathematicians and engineers interested in theoretical foundations of various methods in general use, particularly splines and wavelets. The exposition contains numerous examples and exercises. Students will find a large number of suggestions for their own investigations.
Author : Christophe Cheverry
Publisher : Springer Nature
ISBN 13 : 3030674622
Total Pages : 258 pages
Book Rating : 4.0/5 (36 download)
Download or read book A Guide to Spectral Theory written by Christophe Cheverry and published by Springer Nature. This book was released on 2021-05-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.
Author : Lloyd N. Trefethen
Publisher : Princeton University Press
ISBN 13 : 0691213100
Total Pages : 626 pages
Book Rating : 4.6/5 (912 download)
Download or read book Spectra and Pseudospectra written by Lloyd N. Trefethen and published by Princeton University Press. This book was released on 2020-05-05 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.
Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 9780821836750
Total Pages : 608 pages
Book Rating : 4.8/5 (367 download)
Download or read book Orthogonal Polynomials on the Unit Circle: Spectral theory written by Barry Simon and published by American Mathematical Soc.. This book was released on 2005 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. This book discusses topics such as asymptotics of Toeplitz determinants (Szego's theorems), and limit theorems for the density of the zeros of orthogonal polynomials.
Author :
Publisher : Academic Press
ISBN 13 : 0080873642
Total Pages : 233 pages
Book Rating : 4.0/5 (88 download)
Download or read book Banach Algebra Techniques in Operator Theory written by and published by Academic Press. This book was released on 1972-10-23 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Banach Algebra Techniques in Operator Theory
Author : Federico Bonetto
Publisher : American Mathematical Soc.
ISBN 13 : 1470436817
Total Pages : 346 pages
Book Rating : 4.4/5 (74 download)
Download or read book Mathematical Problems in Quantum Physics written by Federico Bonetto and published by American Mathematical Soc.. This book was released on 2018-10-24 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the QMATH13: Mathematical Results in Quantum Physics conference, held from October 8–11, 2016, at the Georgia Institute of Technology, Atlanta, Georgia. In recent years, a number of new frontiers have opened in mathematical physics, such as many-body localization and Schrödinger operators on graphs. There has been progress in developing mathematical techniques as well, notably in renormalization group methods and the use of Lieb–Robinson bounds in various quantum models. The aim of this volume is to provide an overview of some of these developments. Topics include random Schrödinger operators, many-body fermionic systems, atomic systems, effective equations, and applications to quantum field theory. A number of articles are devoted to the very active area of Schrödinger operators on graphs and general spectral theory of Schrödinger operators. Some of the articles are expository and can be read by an advanced graduate student.
Author : Marius Mantoiu
Publisher : Birkhäuser
ISBN 13 : 3319299921
Total Pages : 259 pages
Book Rating : 4.3/5 (192 download)
Download or read book Spectral Theory and Mathematical Physics written by Marius Mantoiu and published by Birkhäuser. This book was released on 2016-06-30 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schrödinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.
Author : Malcolm Brown
Publisher : Springer Nature
ISBN 13 : 3031311396
Total Pages : 731 pages
Book Rating : 4.0/5 (313 download)
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.
Author : Dario A. Bini
Publisher : Birkhäuser
ISBN 13 : 3319491822
Total Pages : 757 pages
Book Rating : 4.3/5 (194 download)
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 757 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.
Author : Manuel Cepedello Boiso
Publisher : Springer Science & Business Media
ISBN 13 : 3034806485
Total Pages : 546 pages
Book Rating : 4.0/5 (348 download)
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.
Author : Heydar Radjavi
Publisher : Springer Science & Business Media
ISBN 13 : 3642655742
Total Pages : 231 pages
Book Rating : 4.6/5 (426 download)
Download or read book Invariant Subspaces written by Heydar Radjavi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a large amount of work on invariant subspaces, motivated by interest in the structure of non-self-adjoint of the results have been obtained in operators on Hilbert space. Some the context of certain general studies: the theory of the characteristic operator function, initiated by Livsic; the study of triangular models by Brodskii and co-workers; and the unitary dilation theory of Sz. Nagy and Foia!? Other theorems have proofs and interest independent of any particular structure theory. Since the leading workers in each of the structure theories have written excellent expositions of their work, (cf. Sz.-Nagy-Foia!? [1], Brodskii [1], and Gohberg-Krein [1], [2]), in this book we have concentrated on results independent of these theories. We hope that we have given a reasonably complete survey of such results and suggest that readers consult the above references for additional information. The table of contents indicates the material covered. We have restricted ourselves to operators on separable Hilbert space, in spite of the fact that most of the theorems are valid in all Hilbert spaces and many hold in Banach spaces as well. We felt that this restriction was sensible since it eases the exposition and since the separable-Hilbert space case of each of the theorems is generally the most interesting and potentially the most useful case.
Author : Ronald G. Douglas
Publisher : Springer Science & Business Media
ISBN 13 : 1461216567
Total Pages : 212 pages
Book Rating : 4.4/5 (612 download)
Download or read book Banach Algebra Techniques in Operator Theory written by Ronald G. Douglas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of certain advanced topics in operator theory, providing the necessary background while assuming only standard senior-first year graduate courses in general topology, measure theory, and algebra. Each chapter ends with source notes which suggest additional reading along with comments on who proved what and when, followed by a large number of problems of varying difficulty. This new edition will appeal to a whole new generation of students seeking an introduction to this topic.
Author : Xia
Publisher : Birkhäuser
ISBN 13 : 3034854358
Total Pages : 256 pages
Book Rating : 4.0/5 (348 download)
Download or read book Spectral Theory of Hyponormal Operators written by Xia and published by Birkhäuser. This book was released on 2013-11-22 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral analysis of linear operators has always been one of the more active and important fields of operator theory, and of extensive interest to many operator theorists. Its devel opments usually are closely related to certain important problems in contemporary mathematics and physics. In the last 20 years, many new theories and interesting results have been discovered. Now, in this direction, the fields are perhaps wider and deeper than ever. This book is devoted to the study of hyponormal and semi-hyponormal operators. The main results we shall present are those of the author and his collaborators and colleagues, as well as some concerning related topics. To some extent, hyponormal and semi-hyponormal opera tors are "close" to normal ones. Although those two classes of operators contain normal operators as a subclass, what we are interested in are, naturally, nonnormal operators in those classes. With the well-studied normal operators in hand, we cer tainly wish to know the properties of hyponormal and semi-hypo normal operators which resemble those of normal operators. But more important than that, the investigations should be concen trated on the phenomena which only occur in the nonnormal cases.
Author : Nikolai K. Nikolski
Publisher : American Mathematical Soc.
ISBN 13 : 0821852655
Total Pages : 458 pages
Book Rating : 4.8/5 (218 download)
Download or read book Operators, Functions, and Systems - An Easy Reading written by Nikolai K. Nikolski and published by American Mathematical Soc.. This book was released on 2010-10-06 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Together with the companion volume by the same author, Operators, Functions, and Systems: An Easy Reading. Volume 1: Hardy, Hankel, and Toeplitz, Mathematical Surveys and Monographs, Vol. 92, AMS, 2002, this unique work combines four major topics of modern analysis and its applications: A. Hardy classes of holomorphic functions, B. Spectral theory of Hankel and Toeplitz operators, C. Function models for linear operators and free interpolations, and D. Infinite-dimensional system theory and signal processing. This volume contains Parts C and D. Function models for linear operators and free interpolations: This is a universal topic and, indeed, is the most influential operator theory technique in the post-spectral-theorem era. In this book, its capacity is tested by solving generalized Carleson-type interpolation problems. Infinite-dimensional system theory and signal processing: This topic is the touchstone of the three previously developed techniques. The presence of this applied topic in a pure mathematics environment reflects important changes in the mathematical landscape of the last 20 years, in that the role of the main consumer and customer of harmonic, complex, and operator analysis has more and more passed from differential equations, scattering theory, and probability to control theory and signal processing. This and the companion volume are geared toward a wide audience of readers, from graduate students to professional mathematicians. They develop an elementary approach to the subject while retaining an expert level that can be applied in advanced analysis and selected applications.
