Introduction to Spectral Theory
With Applications to Schrödinger Operators
Published on 16. November 1995
Book
Hardback
IX, 338 pages
978-0-387-94501-9 (ISBN)
Description
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 .
(c) 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.
(c) 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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Series
Edition
1996 ed.
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
IX, 338 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 24 mm
Weight
694 gr
ISBN-13
978-0-387-94501-9 (9780387945019)
DOI
10.1007/978-1-4612-0741-2
Schweitzer Classification
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E-Book
12/2012
Springer
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10/2012
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Content
1 The Spectrum of Linear Operators and Hilbert Spaces.- 2 The Geometry of a Hilbert Space and Its Subspaces.- 3 Exponential Decay of Eigenfunctions.- 4 Operators on Hilbert Spaces.- 5 Self-Adjoint Operators.- 6 Riesz Projections and Isolated Points of the Spectrum.- 7 The Essential Spectrum: Weyl's Criterion.- 8 Self-Adjointness: Part 1. The Kato Inequality.- 9 Compact Operators.- 10 Locally Compact Operators and Their Application to Schrödinger Operators.- 11 Semiclassical Analysis of Schrödinger Operators I: The Harmonic Approximation.- 12 Semiclassical Analysis of Schrödinger Operators II: The Splitting of Eigenvalues.- 13 Self-Adjointness: Part 2. The Kato-Rellich Theorem 131.- 14 Relatively Compact Operators and the Weyl Theorem.- 15 Perturbation Theory: Relatively Bounded Perturbations.- 16 Theory of Quantum Resonances I: The Aguilar-Balslev-Combes-Simon Theorem.- 17 Spectral Deformation Theory.- 18 Spectral Deformation of Schrödinger Operators.- 19 The General Theory of Spectral Stability.- 20 Theory of Quantum Resonances II: The Shape Resonance Model.- 21 Quantum Nontrapping Estimates.- 22 Theory of Quantum Resonances III: Resonance Width.- 23 Other Topics in the Theory of Quantum Resonances.- Appendix 1. Introduction to Banach Spaces.- A1.1 Linear Vector Spaces and Norms.- A1.2 Elementary Topology in Normed Vector Spaces.- A1.3 Banach Spaces.- A1.4 Compactness.- 1. Density results.- 2. The Hölder Inequality.- 3. The Minkowski Inequality.- 4. Lebesgue Dominated Convergence.- Appendix 3. Linear Operators on Banach Spaces.- A3.1 Linear Operators.- A3.2 Continuity and Boundedness of Linear Operators.- A3.3 The Graph of an Operator and Closure.- A3.4 Inverses of Linear Operators.- A3.5 Different Topologies on L(X).- Appendix 4. The Fourier Transform, SobolevSpaces, and Convolutions.- A4.1 Fourier Transform.- A4.2 Sobolev Spaces.- A4.3 Convolutions.- References.