UID:
almahu_9947366970002882
Umfang:
1 online resource (329 p.)
Ausgabe:
Rev. ed.
ISBN:
1-281-76657-7
,
9786611766573
,
0-08-087338-3
Serie:
Pure and applied mathematics ; v. 26
Inhalt:
This revised edition of a classic book, which established scattering theory as an important and fruitful area of research, reflects the wealth of new results discovered in the intervening years. This new, revised edition should continue to inspire researchers to expand the application of the original ideas proposed by the authors.
Anmerkung:
Description based upon print version of record.
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Front Cover; Scattering Theory; Copyright Page; Contents; Preface to the Revised Edition; Preface to the First Edition; Chapter I. Introduction; 1. The Dynamic Approach; 2. Scattering Theory Formulated in Terms of Representation Theory; 3. A Semigroup of Operators Related to the Scattering Matrix; 4. The Form of the Scattering Matrix; 5. A Simple Example; 6. Scattering Theory for Transport Phenomena; 7. Notes and Remarks; Chapter II. Representation Theory and the Scattering Operator; 1. The Discrete Case; 2. The Scattering Operator in the Discrete Case; 3. The Continuous Case
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4. The Scattering Operator in the Continuous Case5. Notes and Remarks; Chapter III. A Semigroup of Operators Related to the Scattering Matrix; 1. The Related Semigroups; 2. On Semigroups of Contraction Operators; 3. Spectral Theory; 4. A Spectral Mapping Theorem; 5. Applications of the Spectral Theory; 6. Equivalent Incoming and Outgoing Representations; 7. Notes and Remarks; Chapter IV. The Translation Representation for the Solution of the Wave Equation in Free Space; 1. The Hilbert Space Ho and the Group {U0(t)}; 2. Spectral and Translation Representations of {U0(t)}
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3. The Operator I Extended to Distributions4. Translation Representation for Outgoing and Incoming Data with Infinite Energy; 5. Notes and Remarks; Chapter V. The Solution of the Wave Equation in an Exterior Domain; 1. The Hilbert Space H and the Group {U(t)}; 2. Energy Decay and Translation Representations; 3. The Semigroup {Z(t)}; 4. The Relation between the Semigroup {Z(t) } and the solutions of the Reduced Wave Equation; 5. The Scattering Matrix; 6. Notes and Remarks
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Chapter VI. Symmetric Hyperbolic Systems, the Acoustic Equation with an Indefinite Energy Form, and the Schrödinger EquationPart 1. Symmetric Hyperbolic Systems; 1. Translation Representation in Free Space; 2. Solutions of Hyperbolic Systems in an Exterior Domain; Part 2. The Acoustic Equation with an Indefinite Energy Form and the Schrödmger Equation; 3. Scattering for the Acoustic Equation with an Indefinite Energy Form; 4. The Schrödinger Scattering Matrix; 5. Notes and Remarks; Appendix 1. Semigroups of Operators; Appendix 2. Energy Decay
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Appendix 3. Energy Decay for Star-Shaped ObstaclesAppendix 4. Scattering Theory for Maxwell's Equations; References; Epilogue; Index; Pure and Applied Mathematics
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English
Weitere Ausg.:
ISBN 0-12-440051-5
Sprache:
Englisch
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