On Spectral Theory Of Elliptic Operators
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On Spectral Theory Of Elliptic Operators
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Author : Youri Egorov
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-07-30
On Spectral Theory Of Elliptic Operators written by Youri Egorov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07-30 with Mathematics categories.
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.
On Spectral Theory Of Elliptic Operators
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Author : Yuri V. Egorov
language : en
Publisher:
Release Date : 1991
On Spectral Theory Of Elliptic Operators written by Yuri V. Egorov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
On Spectral Theory Of Elliptic Operators
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Author : Yuri V. Egorov
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
On Spectral Theory Of Elliptic Operators written by Yuri V. Egorov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Elliptic Differential Operators And Spectral Analysis
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Author : D. E. Edmunds
language : en
Publisher: Springer
Release Date : 2018-11-20
Elliptic Differential Operators And Spectral Analysis written by D. E. Edmunds and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-20 with Mathematics categories.
This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature. Starting with the basics of elliptic operators and their naturally associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included. Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.
Pseudodifferential Operators And Spectral Theory
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Author : M.A. Shubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
Pseudodifferential Operators And Spectral Theory written by M.A. Shubin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.
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.
An Introduction To Spectral Theory
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Author : Andrei Giniatoulline
language : en
Publisher: R.T. Edwards, Inc.
Release Date : 2005
An Introduction To Spectral Theory written by Andrei Giniatoulline and has been published by R.T. Edwards, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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.
Spectral Theory And Differential Operators
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Author : E. Brian Davies
language : en
Publisher: Cambridge University Press
Release Date : 1995
Spectral Theory And Differential Operators written by E. Brian Davies and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
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.
Spectral Theory And Differential Operators
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Author : David Edmunds
language : en
Publisher: Oxford University Press
Release Date : 2018-05-03
Spectral Theory And Differential Operators written by David Edmunds and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-03 with Mathematics categories.
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.
Spectral Theory Function Spaces And Inequalities
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Author : B. Malcolm Brown
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-06
Spectral Theory Function Spaces And Inequalities written by B. Malcolm Brown and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-06 with Mathematics categories.
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.
Spectral Theory Of Differential Operators
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Author : V.A. Il'in
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Spectral Theory Of Differential Operators written by V.A. Il'in and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In this fully-illustrated textbook, the author examines the spectral theory of self-adjoint elliptic operators. Chapters focus on the problems of convergence and summability of spectral decompositions about the fundamental functions of elliptic operators of the second order. The author's work offers a novel method for estimation of the remainder term of a spectral function and its Riesz means without recourse to the traditional Carleman technique and Tauberian theorem apparatus.