Distribution of resonances in scattering by thin barriers / Jeffrey Galkowski.

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Bibliographic Details
Main Author:	Galkowski, Jeffrey (Author)
Format:	eBook
Language:	English
Published:	Providence, RI : American Mathematical Society, 2019.
Series:	Memoirs of the American Mathematical Society ; no. 1248.
Subjects:	Mathematical physics. Física matemática Mathematical physics
Online Access:	Click for online access

Table of 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.

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