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Spectral analysis of relativistic operators /

Over the last decade, there has been considerable interest and progress in determining the spectral properties of various operators that take relativistic effects into account, with important implications for mathematics and physics. Difficulties are encountered in many-particle problems due to the...

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Bibliographic Details
Main Authors: Balinsky, A. A. Alexander A
Corporate Authors: World Scientific Firm
Group Author: Evans, W. D
Published: Imperial College Press ; Distributed by World Scientific Pub. Co.,
Publisher Address: London : Singapore :
Publication Dates: 2011.
Literature type: eBook
Language: English
Subjects:
Operator theory
Spectral theory Mathematics
Electronic books
Online Access: http://www.worldscientific.com/worldscibooks/10.1142/P566#t=toc
Summary: Over the last decade, there has been considerable interest and progress in determining the spectral properties of various operators that take relativistic effects into account, with important implications for mathematics and physics. Difficulties are encountered in many-particle problems due to the lack of semiboundedness of the Dirac operator, and this has led to the investigation of operators like those of Chandrasekhar-Herbst and Brown-Ravenhall, which are semibounded under appropriate circumstances. This book contains an up-to-date, comprehensive and self-contained analysis of the spectr
Carrier Form: 1 online resource (xii,186pages)
Bibliography: Includes bibliographical references (pages 177-182) and index.
ISBN: 9781848162198 (electronic bk.)
CLC: O177
Contents: 1. Preliminaries. 1.1. Linear operators. 1.2. Quadratic forms. 1.3. Spectra of self-adjoint operators. 1.4. Compact operators. 1.5. Fourier and Mellin transforms. 1.6. Sobolev spaces. 1.7. Inequalities. 1.8. CLR and related inequalities. 1.9. Lieb-Thirring inequalities -- 2. Operators. 2.1. The Dirac operator. 2.2. The quasi-relativistic operator. 2.3. The Brown-Ravenhall operator. 2.4. A unique continuation property -- 3. Spectra. 3.1. The Dirac operator. 3.2. The quasi-relativistic operator. 3.3. The Brown-Ravenhall operator. 3.4. The absence of embedded eigenvalues -- 4. Miscellany. 4.1.

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