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Softcover ISBN:  9781470435721 
Product Code:  MEMO/259/1248 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
eBook ISBN:  9781470452513 
Product Code:  MEMO/259/1248.E 
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MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
Softcover ISBN:  9781470435721 
eBook ISBN:  9781470452513 
Product Code:  MEMO/259/1248.B 
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MAA Member Price:  $145.80 $109.35 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 259; 2019; 152 ppMSC: Primary 35; 31; Secondary 45; 47
The author studies high energy resonances for the operators \[\Delta_{\partial\Omega,\delta}:=\Delta +\delta_{\partial\Omega}\otimes V\quad \textrm{and}\quad \Delta_{\partial\Omega,\delta'}:=\Delta+\delta_{\partial\Omega}'\otimes V\partial_\nu\] where \(\Omega\subset{\mathbb{R}}^{d}\) is strictly convex with smooth boundary, \(V:L^{2}(\partial\Omega)\to L^{2}(\partial\Omega)\) may depend on frequency, and \(\delta_{\partial\Omega}\) is the surface measure on \(\partial\Omega\).

Table of Contents

Chapters

Acknowledgements

1. Introduction

2. Preliminaries

3. Meromorphic Continuation of the Resolvent

4. Boundary Layer Operators

5. Dynamical Resonance Free Regions

6. Existence of Resonances for the Delta Potential

A. Model Cases

B. Semiclassical Intersecting Lagrangian Distributions

C. The Semiclassical Melrose–Taylor Parametrix


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The author studies high energy resonances for the operators \[\Delta_{\partial\Omega,\delta}:=\Delta +\delta_{\partial\Omega}\otimes V\quad \textrm{and}\quad \Delta_{\partial\Omega,\delta'}:=\Delta+\delta_{\partial\Omega}'\otimes V\partial_\nu\] where \(\Omega\subset{\mathbb{R}}^{d}\) is strictly convex with smooth boundary, \(V:L^{2}(\partial\Omega)\to L^{2}(\partial\Omega)\) may depend on frequency, and \(\delta_{\partial\Omega}\) is the surface measure on \(\partial\Omega\).

Chapters

Acknowledgements

1. Introduction

2. Preliminaries

3. Meromorphic Continuation of the Resolvent

4. Boundary Layer Operators

5. Dynamical Resonance Free Regions

6. Existence of Resonances for the Delta Potential

A. Model Cases

B. Semiclassical Intersecting Lagrangian Distributions

C. The Semiclassical Melrose–Taylor Parametrix