Introduction to Spectral Theory

With Applications to Schrodinger Operators

By: I.M. Sigal, P.D. Hislop

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Hardcover | 16 November 1995

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to Spectral Theory With Applications to Schr6dinger Operators Springer I.M. Sigal P.D. Hislop Department of Mathematics Department of Mathematics University of Kentucky University of Toronto Toronto, Ontario M5S lAI Lexington, KY 40506-0027 USA Canada Editors J .E. Marsden L. Sirovich Control and Dynamical Systems 104-44 Division of Applied Mathematics California 1 nstitute of Technology Brown University Pasadena, CA 91125 Providence, RI 02912 USA USA Mathematics Subject Classification (1991): S1Q05, 35JIO, 35Q55 LJbrary of Congress Cataloging-in-Publication Data Hislop, P.D., 1955- Introduction to spectrallheory : with applications 10 Schrodinger operators I P.D. Hislop, l.M. Siga!. p. cm. - (Applied mathematical sciences ; v. 113) lncludes bibliographical references (p. ) and index. ISBN 978-1-4612-6888-8 ISBN 978-1-4612-0741-2 (eBook) DOI 10.1007/978-1-4612-0741-2 1. Schr6dinger operalors. 2. Spectraltheory (Mathematics) I. Siga1, hrael Michae!, 1945- . II. Title. III. Series: Applied mathematlcal sclem:es (Springer-Verlag New York Inc.) ; v. 113. QA1. A647 voI. 113 IQC 174.17. S3j 510 s-de20 [515 '7223[ 95-12926 Pri nte d o n acid -free paper . © 1996 Springer Science+Business Media New York Originally published by Springer-Verlag New Vork in 1996 Softcover reprint ofthe hardcover 15t edition 1996 AII rights reserved. This work may not be translated or copied in whole or in part without the written permission ofthe publisher Springer Science+Business Media, LLC, except for brief excerpts in connection with reviews or scholarly analysis.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Differential Calculus & Equations Engineering & Technology Technology in General Maths for Engineers Science Science in General Maths for Scientists Applied Mathematics

Engineering in General

Introduction and Overview	p. 1
The Spectrum of Linear Operators and Hilbert Spaces	p. 9
The Geometry of a Hilbert Space and Its Subspaces	p. 17
Exponential Decay of Eigenfunctions	p. 27
Operators on Hilbert Spaces	p. 39
Self-Adjoint Operators	p. 49
Riesz Projections and Isolated Points of the Spectrum	p. 59
The Essential Spectrum: Weyl's Criterion	p. 69
Self-Adjointness: Part 1. The Kato Inequality	p. 77
Compact Operators	p. 89
Locally Compact Operators and Their Application to Schrodinger Operators	p. 99
Semiclassical Analysis of Schrodinger Operators I: The Harmonic Approximation	p. 109
Semiclassical Analysis of Schrodinger Operators II: The Splitting of Eigenvalues	p. 119
Self-Adjointness: Part 2. The Kato - Rellich Theorem	p. 131
Relatively Compact Operators and the Weyl Theorem	p. 139
Perturbation Theory: Relatively Bounded Perturbations	p. 149
Theory of Quantum Resonances I: The Aguilar-Balslev-Combes-Simon Theorem	p. 161
Spectral Deformation Theory	p. 177
Spectral Deformation of Schrodinger Operators	p. 187
The General Theory of Spectral Stability	p. 197
Theory of Quantum Resonances II: The Shape Resonance Model	p. 215
Quantum Nontrapping Estimates	p. 235
Theory of Quantum Resonances III: Resonance Width	p. 251
Other Topics in the Theory of Quantum Resonances	p. 263
Appendix 1. Introduction to Banach Spaces	p. 285
Appendix 2. The Banach Spaces [actual symbol not reproducible]	p. 293
Appendix 3. Linear Operators on Banach Spaces	p. 301
Appendix 4. The Fourier Transform, Sobolev Spaces, and Convolutions	p. 313
References	p. 319
Index	p. 333
Table of Contents provided by Blackwell. All Rights Reserved.

Introduction to Spectral Theory

With Applications to Schrodinger Operators

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Hardcover

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