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Spectral Theory Function Spaces And Inequalities
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Book Synopsis Spectral Theory, Function Spaces and Inequalities by : B. Malcolm Brown
Download or read book Spectral Theory, Function Spaces and Inequalities written by B. Malcolm Brown and published by Springer Science & Business Media. This book was released on 2011-11-06 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.
Book Synopsis Spectral Theory, Function Spaces and Inequalities by : B. Malcolm Brown
Download or read book Spectral Theory, Function Spaces and Inequalities written by B. Malcolm Brown and published by Birkhäuser. This book was released on 2011-11-09 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.
Book Synopsis Spectral Theory and Differential Operators by : David Eric Edmunds
Download or read book Spectral Theory and Differential Operators written by David Eric Edmunds and published by Oxford University Press. This book was released on 2018 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.
Book Synopsis The Structure of Functions by : Hans Triebel
Download or read book The Structure of Functions written by Hans Triebel and published by Birkhäuser. This book was released on 2012-12-06 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications. The first chapter is devoted to a detailed study of quarkonial (subatomic) decompositions of functions and distributions on euclidean spaces, domains, manifolds and fractals. This approach combines the advantages of atomic and wavelet representations. It paves the way to sharp inequalities and embeddings in function spaces, spectral theory of fractal elliptic operators, and a regularity theory of some semi-linear equations. The book is self-contained, although some parts may be considered as a continuation of the author's book "Fractals and Spectra" (MMA 91). It is directed to mathematicians and (theoretical) physicists interested in the topics indicated and, in particular, how they are interrelated.
Book Synopsis Operator Theory in Function Spaces and Banach Lattices by : C.B. Huijsmans
Download or read book Operator Theory in Function Spaces and Banach Lattices written by C.B. Huijsmans and published by Birkhäuser. This book was released on 2012-12-06 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to A.C. Zaanen, one of the pioneers of functional analysis, and eminent expert in modern integration theory and the theory of vector lattices, on the occasion of his 80th birthday. The book opens with biographical notes, including Zaanen's curriculum vitae and list of publications. It contains a selection of original research papers which cover a broad spectrum of topics about operators and semigroups of operators on Banach lattices, analysis in function spaces and integration theory. Special attention is paid to the spectral theory of operators on Banach lattices; in particular, to the one of positive operators. Classes of integral operators arising in systems theory, optimization and best approximation problems, and evolution equations are also discussed. The book will appeal to a wide range of readers engaged in pure and applied mathematics.
Book Synopsis An Introduction to Spectral Theory by : Andrei Giniatoulline
Download or read book An Introduction to Spectral Theory written by Andrei Giniatoulline and published by R.T. Edwards, Inc.. This book was released on 2005 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brief and accessible introduction to the spectral theory of linear second order elliptic differential operators. By introducing vital topics of abstract functional analysis where necessary, and using clear and simple proofs, the book develops an elegant presentation of the theory while integrating applications of basic real world problems involving the Laplacian. Suitable for use as a self-contained introduction for beginners or as a one-semester student text; contains some 25 examples and 60 exercises, most with detailed hints.
Book Synopsis Fractals and Spectra by : Hans Triebel
Download or read book Fractals and Spectra written by Hans Triebel and published by Springer Science & Business Media. This book was released on 2010-10-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Most of the presented material is published here for the first time.
Book Synopsis Functional Inequalities Markov Semigroups and Spectral Theory by : Fengyu Wang
Download or read book Functional Inequalities Markov Semigroups and Spectral Theory written by Fengyu Wang and published by Elsevier. This book was released on 2006-04-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the functional inequalities are introduced to describe:(i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap;(ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density;(iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.
Book Synopsis A Guide to Spectral Theory by : Christophe Cheverry
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.
Download or read book Sobolev Spaces written by Vladimir Maz'ya and published by Springer Science & Business Media. This book was released on 2011-02-11 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a significantly augmented list of references aim to create a broader and modern view of the area.
Book Synopsis Around the Research of Vladimir Maz'ya I by : Ari Laptev
Download or read book Around the Research of Vladimir Maz'ya I written by Ari Laptev and published by Springer Science & Business Media. This book was released on 2009-12-02 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known and often play a key role in the study of different aspects of the theory, which is demonstrated, in particular, by presented new results and reviews from world-recognized specialists. Sobolev type spaces, extensions, capacities, Sobolev inequalities, pseudo-Poincare inequalities, optimal Hardy-Sobolev-Maz'ya inequalities, Maz'ya's isocapacitary inequalities in a measure-metric space setting and many other actual topics are discussed.
Book Synopsis On Spectral Theory of Elliptic Operators by : Youri Egorov
Download or read book On Spectral Theory of Elliptic Operators written by Youri Egorov and published by Springer Science & Business Media. This book was released on 1996-07-30 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that a wealth of problems of different nature, applied as well as purely theoretic, can be reduced to the study of elliptic equations and their eigen-values. During the years many books and articles have been published on this topic, considering spectral properties of elliptic differential operators from different points of view. This is one more book on these properties. This book is devoted to the study of some classical problems of the spectral theory of elliptic differential equations. The reader will find hardly any intersections with the books of Shubin [Sh] or Rempel-Schulze [ReSch] or with the works cited there. This book also has no general information in common with the books by Egorov and Shubin [EgShu], which also deal with spectral properties of elliptic operators. There is nothing here on oblique derivative problems; the reader will meet no pseudodifferential operators. The main subject of the book is the estimates of eigenvalues, especially of the first one, and of eigenfunctions of elliptic operators. The considered problems have in common the approach consisting of the application of the variational principle and some a priori estimates, usually in Sobolev spaces. In many cases, impor tant for physics and mechanics, as well as for geometry and analysis, this rather elementary approach allows one to obtain sharp results.
Book Synopsis Spectral Theory and Geometry by : E. Brian Davies
Download or read book Spectral Theory and Geometry written by E. Brian Davies and published by Cambridge University Press. This book was released on 1999-09-30 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authoritative lectures from world experts on spectral theory and geometry.
Book Synopsis Spectral Theory of Operators in Hilbert Space by : Kurt O. Friedrichs
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.
Book Synopsis Operator Theory in Function Spaces and Banach Lattices by : C.B. Huijsmans
Download or read book Operator Theory in Function Spaces and Banach Lattices written by C.B. Huijsmans and published by Birkhäuser. This book was released on 1995-01-27 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to A.C. Zaanen, one of the pioneers of functional analysis, and eminent expert in modern integration theory and the theory of vector lattices, on the occasion of his 80th birthday. The book opens with biographical notes, including Zaanen's curriculum vitae and list of publications. It contains a selection of original research papers which cover a broad spectrum of topics about operators and semigroups of operators on Banach lattices, analysis in function spaces and integration theory. Special attention is paid to the spectral theory of operators on Banach lattices; in particular, to the one of positive operators. Classes of integral operators arising in systems theory, optimization and best approximation problems, and evolution equations are also discussed. The book will appeal to a wide range of readers engaged in pure and applied mathematics.
Book Synopsis A Short Course on Spectral Theory by : William Arveson
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.
Book Synopsis Spectral Theory of Self-Adjoint Operators in Hilbert Space by : Michael Sh. Birman
Download or read book Spectral Theory of Self-Adjoint Operators in Hilbert Space written by Michael Sh. Birman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: It isn't that they can't see the solution. It is Approach your problems from the right end that they can't see the problem. and begin with the answers. Then one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be com pletely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order" , which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
