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Softcover ISBN: | 978-1-4704-3572-1 |
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Softcover ISBN: | 978-1-4704-3572-1 |
Product Code: | MEMO/259/1248 |
List Price: | $81.00 |
MAA Member Price: | $72.90 |
AMS Member Price: | $48.60 |
eBook ISBN: | 978-1-4704-5251-3 |
Product Code: | MEMO/259/1248.E |
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Softcover ISBN: | 978-1-4704-3572-1 |
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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 \(\partial\Omega\).
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Table of Contents
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Chapters
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Acknowledgements
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1. Introduction
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2. Preliminaries
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3. Meromorphic Continuation of the Resolvent
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4. Boundary Layer Operators
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5. Dynamical Resonance Free Regions
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6. Existence of Resonances for the Delta Potential
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A. Model Cases
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B. Semiclassical Intersecting Lagrangian Distributions
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C. The Semiclassical Melrose–Taylor Parametrix
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Additional Material
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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