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On Spectral Theory Of Elliptic Operators
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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 On Spectral Theory of Elliptic Operators by : Yuri V. Egorov
Download or read book On Spectral Theory of Elliptic Operators written by Yuri V. Egorov and published by Birkhäuser. This book was released on 2012-12-06 with total page 336 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 On Spectral Theory of Elliptic Operators by : Yuri V. Egorov
Download or read book On Spectral Theory of Elliptic Operators written by Yuri V. Egorov and published by . This book was released on 1991 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elliptic Differential Operators and Spectral Analysis by : D. E. Edmunds
Download or read book Elliptic Differential Operators and Spectral Analysis written by D. E. Edmunds and published by Springer. This book was released on 2018-11-20 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Spectral Theory and Differential Operators by : David Edmunds
Download or read book Spectral Theory and Differential Operators written by David Edmunds and published by Oxford University Press. This book was released on 2018-05-03 with total page 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 Spectral Theory and Differential Operators by : E. Brian Davies
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.
Book Synopsis Partial Differential Equations VII by : M.A. Shubin
Download or read book Partial Differential Equations VII written by M.A. Shubin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Also including a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum".
Book Synopsis Pseudodifferential Operators and Spectral Theory by : M.A. Shubin
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.
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 Spectral Theory of Differential Operators by : V.A. Il'in
Download or read book Spectral Theory of Differential Operators written by V.A. Il'in and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Microlocal Analysis and Spectral Theory of Elliptic Operators on Non-compact Manifolds by :
Download or read book Microlocal Analysis and Spectral Theory of Elliptic Operators on Non-compact Manifolds written by and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 . This book was released on 1987 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and long-awaited volume provides an up-to-date account of those parts of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. For the first time it brings together recent results in essential spectra, measures of non-compactness, entropy numbers, approximation numbers, eigenvalues, and the relationships among these concepts. The authors illustrate abstract theory with results for embedding maps between Sobolev spaces. Strong emphasis is placed on application to boundary-value problems for general second-order linear elliptic equations in an arbitrary domain in Rn. The book introduces some key eastern European work, never before available in English translation.
Book Synopsis Inverse Spectral Theory and Relative Determinants of Elliptic Operators by : Clara Lucía Aldana Domínguez
Download or read book Inverse Spectral Theory and Relative Determinants of Elliptic Operators written by Clara Lucía Aldana Domínguez and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 On the Spectral Theory of Invariant Elliptic Operators on Compact G-manifolds by : Thomas Donaldson
Download or read book On the Spectral Theory of Invariant Elliptic Operators on Compact G-manifolds written by Thomas Donaldson and published by . This book was released on 1978 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pseudodifferential Operators and Spectral Theory by : Mikhail A. Shubin
Download or read book Pseudodifferential Operators and Spectral Theory written by Mikhail A. Shubin and published by Springer. This book was released on 1987 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of pseudo differential operators (abbreviated PD~) is compara tively young; in its modern form it was created in the mid-sixties. The progress achieved with its help, however, has been so essential that without PD~ it would indeed be difficult to picture modern analysis and mathematical physics. PD~ are of particular importance in the study of elliptic equations. Even the simplest operations on elliptic operators (e. g. taking the inverse or the square root) lead out of the class of differential operators but will, under reasonable assumptions, preserve the class of PD~. A significant role is played by PD~ in the index theory for elliptic operators, where PD~ are needed to extend the class of possible deformations of an operator. PD~ appear naturally in the reduction to the boundary for any elliptic boundary problem. In this way, PD~ arise not as an end-in-themselves, but as a powerful and natural tool for the study of partial differential operators (first and foremost elliptic and hypo elliptic ones). In many cases, PD~ allow us not only to establish new theorems but also to have a fresh look at old ones and thereby obtain simpler and more transparent formulations of already known facts. This is, for instance, the case in the theory of Sobolev spaces. A natural generalization of PD~ are the Fourier integral operators (abbreviatedFIO), the first version ofwhich was the Maslov canonical operator.
Book Synopsis Inverse Spectral Theory and Relative Determinants of Elliptic Operators on Surfaces with Cusps by : Clara Lucía Aldana Domínguez
Download or read book Inverse Spectral Theory and Relative Determinants of Elliptic Operators on Surfaces with Cusps written by Clara Lucía Aldana Domínguez and published by . This book was released on 2009 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
