Download or read book Spectral Theory and Applications of Linear Operators and Block Operator Matrices written by Aref Jeribi and published by Springer. This book was released on 2015-07-04 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.
Download or read book Summability Through Functional Analysis written by A. Wilansky and published by Elsevier. This book was released on 2000-04-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summability is an extremely fruitful area for the application of functional analysis; this volume could be used as a source for such applications. Those parts of summability which only have ``hard'' (classical) proofs are omitted; the theorems given all have ``soft'' (functional analytic) proofs.
Download or read book Linear Operators and Matrices written by Israel Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: In September 1998, during the 'International Workshop on Analysis and Vibrat ing Systems' held in Canmore, Alberta, Canada, it was decided by a group of participants to honour Peter Lancaster on the occasion of his 70th birthday with a volume in the series 'Operator Theory: Advances and Applications'. Friends and colleagues responded enthusiastically to this proposal and within a short time we put together the volume which is now presented to the reader. Regarding accep tance of papers we followed the usual rules of the journal 'Integral Equations and Operator Theory'. The papers are dedicated to different problems in matrix and operator theory, especially to the areas in which Peter contributed so richly. At our request, Peter agreed to write an autobiographical paper, which appears at the beginning of the volume. It continues with the list of Peter's publications. We believe that this volume will pay tribute to Peter on his outstanding achievements in different areas of mathematics. 1. Gohberg, H. Langer P ter Lancast r *1929 Operator Theory: Advances and Applications, Vol. 130, 1- 7 © 2001 Birkhiiuser Verlag Basel/Switzerland My Life and Mathematics Peter Lancaster I was born in Appleby, a small county town in the north of England, on November 14th, 1929. I had two older brothers and was to have one younger sister. My family moved around the north of England as my father's work in an insurance company required.
Download or read book Simultaneous Triangularization written by Heydar Radjavi and published by Springer. This book was released on 2012-11-19 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is designed to appeal to two different, yet intersecting audiences: linear algebraists and operator theorists. The first half contains a thorough treatment of classical and recent results on triangularization of collections of matrices, while the remainder describes what is known about extensions to linear operators on Banach spaces. It will thus be useful to everyone interested in matrices or operators since the results involve many other topics.
Download or read book Operator Theory Operator Algebras and Matrix Theory written by Carlos André and published by Birkhäuser. This book was released on 2018-08-22 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.
Download or read book Numerical Range written by Karl E. Gustafson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region.
Download or read book Products of Random Matrices with Applications to Schr dinger Operators written by P. Bougerol and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: CHAPTER I THE DETERMINISTIC SCHRODINGER OPERATOR 187 1. The difference equation. Hyperbolic structures 187 2. Self adjointness of H. Spectral properties . 190 3. Slowly increasing generalized eigenfunctions 195 4. Approximations of the spectral measure 196 200 5. The pure point spectrum. A criterion 6. Singularity of the spectrum 202 CHAPTER II ERGODIC SCHRÖDINGER OPERATORS 205 1. Definition and examples 205 2. General spectral properties 206 3. The Lyapunov exponent in the general ergodie case 209 4. The Lyapunov exponent in the independent eas e 211 5. Absence of absolutely continuous spectrum 221 224 6. Distribution of states. Thouless formula 232 7. The pure point spectrum. Kotani's criterion 8. Asymptotic properties of the conductance in 234 the disordered wire CHAPTER III THE PURE POINT SPECTRUM 237 238 1. The pure point spectrum. First proof 240 2. The Laplace transform on SI(2,JR) 247 3. The pure point spectrum. Second proof 250 4. The density of states CHAPTER IV SCHRÖDINGER OPERATORS IN A STRIP 2';3 1. The deterministic Schrödinger operator in 253 a strip 259 2. Ergodie Schrödinger operators in a strip 3. Lyapunov exponents in the independent case. 262 The pure point spectrum (first proof) 267 4. The Laplace transform on Sp(~,JR) 272 5. The pure point spectrum, second proof vii APPENDIX 275 BIBLIOGRAPHY 277 viii PREFACE This book presents two elosely related series of leetures. Part A, due to P.
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 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new concepts in operator theory and covers classes of operators (in particular, non-selfadjoint operators) which exhibit various interesting phenomena. Special attention is paid to applications in many areas of mathematical physics, including quantum mechanics, fluid mechanics, and magnetohydrodynamics.The author also discusses an operator theoretic approach to spectral problems for linear operators admitting a certain block structure. The results apply to bounded or finite-dimensional operators like block matrices as well to unbounded operators describing systems of differential equations. New concepts of numerical range are developed.
Download or read book Traces and Determinants of Linear Operators written by Israel Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to a theory of traces and determinants on embedded algebras of linear operators, where the trace and determinant are extended from finite rank operators by a limit process. The self-contained material should appeal to a wide group of mathematicians and engineers, and is suitable for teaching.
Download or read book Perturbation theory for linear operators written by Tosio Kato and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Limit Operators Collective Compactness and the Spectral Theory of Infinite Matrices written by Simon N. Chandler-Wilde and published by American Mathematical Soc.. This book was released on 2011 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first half of this memoir the authors explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). They build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator $A$ (its operator spectrum). In the second half of this memoir the authors study bounded linear operators on the generalised sequence space $\ell^p(\mathbb{Z}^N,U)$, where $p\in [1,\infty]$ and $U$ is some complex Banach space. They make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator $A$ is a locally compact perturbation of the identity. Especially, they obtain stronger results than previously known for the subtle limiting cases of $p=1$ and $\infty$.
Download or read book Matrix and Operator Equations and Applications written by Mohammad Sal Moslehian and published by Springer Nature. This book was released on 2023-07-29 with total page 763 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns matrix and operator equations that are widely applied in various disciplines of science to formulate challenging problems and solve them in a faithful way. The main aim of this contributed book is to study several important matrix and operator equalities and equations in a systematic and self-contained fashion. Some powerful methods have been used to investigate some significant equations in functional analysis, operator theory, matrix analysis, and numerous subjects in the last decades. The book is divided into two parts: (I) Matrix Equations and (II) Operator Equations. In the first part, the state-of-the-art of systems of matrix equations is given and generalized inverses are used to find their solutions. The semi-tensor product of matrices is used to solve quaternion matrix equations. The contents of some chapters are related to the relationship between matrix inequalities, matrix means, numerical range, and matrix equations. In addition, quaternion algebras and their applications are employed in solving some famous matrix equations like Sylvester, Stein, and Lyapunov equations. A chapter devoted to studying Hermitian polynomial matrix equations, which frequently arise from linear-quadratic control problems. Moreover, some classical and recently discovered inequalities for matrix exponentials are reviewed. In the second part, the latest developments in solving several equations appearing in modern operator theory are demonstrated. These are of interest to a wide audience of pure and applied mathematicians. For example, the Daugavet equation in the linear and nonlinear setting, iterative processes and Volterra-Fredholm integral equations, semicircular elements induced by connected finite graphs, free probability, singular integral operators with shifts, and operator differential equations closely related to the properties of the coefficient operators in some equations are discussed. The chapters give a comprehensive account of their subjects. The exhibited chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.
Download or read book Operators on Hilbert Space written by V. S. Sunder and published by Springer. This book was released on 2016-08-05 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators.
Download or read book The Random Matrix Theory of the Classical Compact Groups written by Elizabeth S. Meckes and published by Cambridge University Press. This book was released on 2019-08-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.
Download or read book Summability Theory and Its Applications written by Feyzi Başar and published by CRC Press. This book was released on 2022-06-27 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summability Theory and Its Applications explains various aspects of summability and demonstrates its applications in a rigorous and coherent manner. The content can readily serve as a reference or as a useful series of lecture notes on the subject. This substantially revised new edition includes brand new material across several chapters as well as several corrections, including: the addition of the domain of Cesaro matrix C(m) of order m in the classical sequence spaces to Chapter 4; and introducing the domain of four-dimensional binomial matrix in the spaces of bounded, convergent in the Pringsheim's sense, both convergent in the Pringsheim's sense and bounded, and regularly convergent double sequences, in Chapter 7. Features Investigates different types of summable spaces and computes their dual Suitable for graduate students and researchers with a (special) interest in spaces of single and double sequences, matrix transformations and domains of triangle matrices Can serve as a reference or as supplementary reading in a computational physics course, or as a key text for special Analysis seminars.
Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2001-08-15 with total page 1017 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.
Download or read book Operator Theory by Example written by Stephan Ramon Garcia and published by Oxford University Press. This book was released on 2023-01-30 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator. The text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well-researched historical facts which place each chapter within the broader context of the development of the field as a whole.
