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Elliptic Differential Operators and Spectral Analysis

2018-11-20 Mathematics
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Release : 2018-11-20
Genre : Mathematics
Kind : eBook
Book Rating : 254/5 ( reviews)

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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. This book was released on 2018-11-20. 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.

On Spectral Theory of Elliptic Operators

1996-07-30 Mathematics
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Release : 1996-07-30
Genre : Mathematics
Kind : eBook
Book Rating : 902/5 ( reviews)

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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. This book was released on 1996-07-30. 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.

On Spectral Theory of Elliptic Operators

1996-07-30
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Release : 1996-07-30
Genre :
Kind : eBook
Book Rating : 304/5 ( reviews)

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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. This book was released on 1996-07-30. Available in PDF, EPUB and Kindle. Book excerpt:

Spectral Analysis of Differential Operators

2005 Mathematics
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Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 454/5 ( reviews)

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Book Synopsis Spectral Analysis of Differential Operators by : Fedor S. Rofe-Beketov

Download or read book Spectral Analysis of Differential Operators written by Fedor S. Rofe-Beketov. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic SchrAdinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators."

Spectral Theory and Differential Operators

1995 Mathematics
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Release : 1995
Genre : Mathematics
Kind : eBook
Book Rating : 105/5 ( reviews)

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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. This book was released on 1995. 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.

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