Download or read book A Spectral Theory Of Noncommuting Operators written by Rongwei Yang and published by Springer Nature. This book was released on with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Theory of Non Self Adjoint Two Point Differential Operators written by John Locker and published by American Mathematical Soc.. This book was released on 2000 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops the spectral theory of an nth order non-self-adjoint two- point differential operator L in the complex Hilbert space L2[0,1]. The differential operator L is determined by an nth order formal differential l and by n linearly independent boundary values B1,.,Bn. Locker first lays the foundations of the spectral theory for closed linear operators and Fredholm operators in Hilbert spaces before developing the spectral theory of the differential operator L. The book is a sequel to Functional analysis and two-point differential operators, 1986. Annotation copyrighted by Book News, Inc., Portland, OR.

Download or read book Spectral Theory of Linear Operators written by Henry R. Dowson and published by . This book was released on 1978 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: General spectral theory; Riesz operators; Hermitian operators; Prespectral operators; Well-bounded operators.

Download or read book Non Selfadjoint Operators in Quantum Physics written by Fabio Bagarello and published by John Wiley & Sons. This book was released on 2015-07-24 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.

Download or read book Spectral Properties of Noncommuting Operators written by Brian R. Jefferies and published by . This book was released on 2014-01-15 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Theory and Differential Operators written by E. Brian Davies and published by Cambridge University Press. This book was released on 1995 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on partial differential operators.

Download or read book The Spectral Theory of Toeplitz Operators written by L. Boutet de Monvel and published by Princeton University Press. This book was released on 1981-08-21 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations. If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol. It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds.

Download or read book A Short Course on Spectral Theory written by William Arveson and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here.

Download or read book Spectral Theory of Linear Operators written by Abram Iezekiilovich Plesner and published by . This book was released on 1969 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Theory of Operators in Hilbert Space written by Kurt O. Friedrichs and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present lectures intend to provide an introduction to the spectral analysis of self-adjoint operators within the framework of Hilbert space theory. The guiding notion in this approach is that of spectral representation. At the same time the notion of function of an operator is emphasized. The formal aspects of these concepts are explained in the first two chapters. Only then is the notion of Hilbert space introduced. The following three chapters concern bounded, completely continuous, and non-bounded operators. Next, simple differential operators are treated as operators in Hilbert space, and the final chapter deals with the perturbation of discrete and continuous spectra. The preparation of the original version of these lecture notes was greatly helped by the assistance of P. Rejto. Various valuable suggestions made by him and by R. Lewis have been incorporated. The present version of the notes contains extensive modifica tions, in particular in the chapters on bounded and unbounded operators. February, 1973 K.O.F. PREFACE TO THE SECOND PRINTING The second printing (1980) is a basically unchanged reprint in which a number of minor errors were corrected. The author wishes to thank Klaus Schmidt (Lausanne) and John Sylvester (New York) for their lists of errors. v TABLE OF CONTENTS I. Spectral Representation 1 1. Three typical problems 1 12 2. Linear space and functional representation.

Download or read book Spectral Properties of Noncommuting Operators written by Brian Jefferies and published by Springer Science & Business Media. This book was released on 2004-05-13 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Forming functions of operators is a basic task of many areas of linear analysis and quantum physics. Weyl’s functional calculus, initially applied to the position and momentum operators of quantum mechanics, also makes sense for finite systems of selfadjoint operators. By using the Cauchy integral formula available from Clifford analysis, the book examines how functions of a finite collection of operators can be formed when the Weyl calculus is not defined. The technique is applied to the determination of the support of the fundamental solution of a symmetric hyperbolic system of partial differential equations and to proving the boundedness of the Cauchy integral operator on a Lipschitz surface.

Download or read book Pseudodifferential Operators and Spectral Theory written by M.A. Shubin and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: I had mixed feelings when I thought how I should prepare the book for the second edition. It was clear to me that I had to correct all mistakes and misprints that were found in the book during the life of the first edition. This was easy to do because the mistakes were mostly minor and easy to correct, and the misprints were not many. It was more difficult to decide whether I should update the book (or at least its bibliography) somehow. I decided that it did not need much of an updating. The main value of any good mathematical book is that it teaches its reader some language and some skills. It can not exhaust any substantial topic no matter how hard the author tried. Pseudodifferential operators became a language and a tool of analysis of partial differential equations long ago. Therefore it is meaningless to try to exhaust this topic. Here is an easy proof. As of July 3, 2000, MathSciNet (the database of the American Mathematical Society) in a few seconds found 3695 sources, among them 363 books, during its search for "pseudodifferential operator". (The search also led to finding 963 sources for "pseudo-differential operator" but I was unable to check how much the results ofthese two searches intersected). This means that the corresponding words appear either in the title or in the review published in Mathematical Reviews.

Download or read book Spectral Theory of Random Schr dinger Operators written by R. Carmona and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians for these systems have a ten dency to have pure point spectrum, especially in low dimension or for large disorder. A lot of effort has been devoted to the mathematical study of the random self-adjoint operators relevant to the theory of localization for disordered systems. It is fair to say that progress has been made and that the un derstanding of the phenomenon has improved. This does not mean that the subject is closed. Indeed, the number of important problems actually solved is not larger than the number of those remaining. Let us mention some of the latter: • A proof of localization at all energies is still missing for two dimen sional systems, though it should be within reachable range. In the case of the two dimensional lattice, this problem has been approached by the investigation of a finite discrete band, but the limiting pro cedure necessary to reach the full two-dimensional lattice has never been controlled. • The smoothness properties of the density of states seem to escape all attempts in dimension larger than one. This problem is particularly serious in the continuous case where one does not even know if it is continuous.

Download or read book Spectral Theory of Schrodinger Operators written by Rafael del Río and published by American Mathematical Soc.. This book was released on 2004 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers the articles based on a series of lectures from a workshop held at the Institute of Applied Mathematics of the National University of Mexico. The aim of the book is to present to a non-specialized audience the basic tools needed to understand and appreciate new trends of research on Schrodinger operator theory. Topics discussed include various aspects of the spectral theory of differential operators, the theory of self-adjoint operators, finite rank perturbations, spectral properties of random Schrodinger operators, and scattering theory for Schrodinger operators. The material is suitable for graduate students and research mathematicians interested in differential operators, in particular, spectral theory of Schrodinger operators.

Download or read book Spectral Theory of Block Operator Matrices and Applications written by Christiane Tretter and published by World Scientific. This book was released on 2008-10-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics. The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic Riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics. Contents:Bounded Block Operator Matrices:The Quadratic Numerical RangeSpecial Classes of Block Operator MatricesSpectral InclusionEstimates of the ResolventCorners of the Quadratic Numerical RangeSchur Complements and Their FactorizationBlock DiagonalizationSpectral Supporting SubspacesVariational Principles for Eigenvalues in GapsJ-Self-Adjoint Block Operator MatricesThe Block Numerical RangeNumerical Ranges of Operator PolynomialsGershgorin's Theorem for Block Operator MatricesUnbounded Block Operator Matrices:Relative Boundedness and Relative CompactnessClosedness and Closability of Block Operator MatricesSpectrum and ResolventThe Essential SpectrumSpectral InclusionSymmetric and J-Symmetric Block Operator MatricesDichotomous Block Operator Matrices and Riccati EquationsBlock Diagonalization and Half Range CompletenessUniqueness Results for Solutions of Riccati EquationsVariational PrinciplesEigenvalue EstimatesApplications in Mathematical Physics:Upper Dominant Block Operator Matrices in MagnetohydrodynamicsDiagonally Dominant Block Operator Matrices in Fluid MechanicsOff-Diagonally Dominant Block Operator Matrices in Quantum Mechanics Readership: Mathematicians, physicists and engineers. Keywords:Operator Theory;Spectral Theory;Eigenvalues;Differential Equations;Riccati Equations;Numerical Range;Mathematical Physics;Matrix TheoryKey Features:Challenging spectral problems to which standard methods do not applyNew results even in the finite dimensional caseMany illustrating examplesWide range of possible applicationsReviews:“This book is a valuable addition to the literature and will be of great help for those working in this field already as well as for people looking for an interesting introduction to the topic.”Mathematical Reviews

Download or read book A Local Spectral Theory for Closed Operators written by Ivan N. Erdelyi and published by Cambridge University Press. This book was released on 1985-08 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which is almost entirely devoted to unbounded operators, gives a unified treatment of the contemporary local spectral theory for unbounded closed operators on a complex Banach space. While the main part of the book is original, necessary background materials provided. There are some completely new topics treated, such as the complete spectral duality theory with the first comprehensive proof of the predual theorem, in two different versions. Also covered are spectral resolvents of various kinds (monotomic, strongly monotonic, almost localized, analytically invariant), and spectral decompositions with respect to the identity. The book concludes with an extensive reference list, including many papers published in the People's Republic of China, here brought to the attention of Western mathematicians for the first time. Pure mathematicians, especially those working in operator theory and functional analysis, will find this book of interest.

Download or read book Spectral Theory of Operators in Hilbert Space written by Kurt Otto Friedrichs and published by . This book was released on 1980 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: