| Description |
1 online resource (168 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society ; number 1248 |
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Memoirs of the American Mathematical Society ; no. 1248.
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| Contents |
Chapter 1. Introduction -- 1.1. Outline of the article -- Chapter 2. Preliminaries -- 2.1. The billiard ball flow and map -- 2.2. Semiclassical preliminaries -- 2.3. The shymbol -- Chapter 3. Meromorphic Continuation of the Resolvent -- 3.1. Formal definition of the operators -- 3.2. Meromorphic continuation of the resolvent -- Chapter 4. Boundary Layer Operators -- 4.1. Classical layer potential theory -- 4.2. High energy estimates on the boundary layer operators -- 4.3. Microlocal description of the free resolvent -- 4.4. Boundary layer operators and potentials away from glancing -- 4.5. Boundary layer operators and potentials near glancingChapter 5. Dynamical Resonance Free Regions -- 5.1. Conjectures and numerical computation of resonances -- 5.2. Outline of the proof and organization of the chapter -- 5.3. Resonance free regions -delta Potential -- 5.4. Resonance free regions -delta prime potential -- Chapter 6. Existence of Resonances for the Delta Potential -- 6.1. Outline of the Proof -- 6.2. Existence for generic domains and potentials -- Appendix A. Model Cases -- A.1. The delta potential -- A.2. The delta prime potential -- Appendix B. Semiclassical Intersecting Lagrangian Distributions -- Appendix C. The Semiclassical Melrose-Taylor Parametrix -- C.1. Construction of the operators _{ } and _{ } -- C.2. Microlocal description of _{ }, _{ } and the Airy multipliers -- C.3. Parametrix for diffractive points -- C.4. Relation with exact operators in gliding case -- C.5. Wave equation parametrices -- C.6. Semiclassical Fourier integral operators with singular phase |
| Notes |
Keywords: Transmission problems, layer potentials, layer operators, high frequency, resonances, potential theory, hypersingular operator |
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"May 2019 - Volume 259 - Number 1248 (fifth of 8 numbers)." |
| Bibliography |
Includes bibliographical references (pages 149-152) |
| Notes |
Online resource; title from PDF title page (viewed August 27, 2019) |
| Subject |
Mathematical physics.
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Física matemática
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Mathematical physics
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| Form |
Electronic book
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| ISBN |
9781470452513 |
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1470452510 |
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1470435721 |
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9781470435721 |
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