Ebook: Microlocal Methods in Mathematical Physics and Global Analysis

Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigorous many ideas that originated in physics. Since then it has grown to a powerful machine which is used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. In this book extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the University of Tübingen from the 14th to the 18th of June 2011, are collected.​

---

Microlocal analysis is a mathematical field that was invented for the detailed investigation of problems from partial differential equations in the mid-20th century and that incorporated and elaborated on many ideas that had originated in physics. Since then, it has grown to a powerful machine used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. This book collects extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the University of T?bingen from June 14th to 18th, 2011.

---

Microlocal analysis is a mathematical field that was invented for the detailed investigation of problems from partial differential equations in the mid-20th century and that incorporated and elaborated on many ideas that had originated in physics. Since then, it has grown to a powerful machine used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. This book collects extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the University of T?bingen from June 14th to 18th, 2011.
Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Local Smoothing with a Prescribed Loss for the Schr?dinger Equation....Pages 3-6
Propagation Through Trapped Sets and Semiclassical Resolvent Estimates....Pages 7-10
Space–Adiabatic Theory for Random–Landau Hamiltonian: Results and Prospects....Pages 11-14
Microlocal Analysis of FIOs with Singularities....Pages 15-17
A Nonlinear Adiabatic Theorem for Coherent States....Pages 19-23
Adiabatic Limits and Related Lattice Point Problems....Pages 25-28
The Effective Hamiltonian in Curved Quantum Waveguides and When It Does Not Work....Pages 29-32
The Adiabatic Limit of the Laplacian on Thin Fibre Bundles....Pages 33-36
Adiabatic Limit with Isolated Degenerate Fibres....Pages 37-43
Microlocal Analysis and Adiabatic Problems: The Case of Perturbed Periodic Schr?dinger Operators....Pages 45-48
Recent Results in Semiclassical Approximation with Rough Potentials....Pages 49-52
Front Matter....Pages 53-53
On the Closure of Elliptic Wedge Operators....Pages 55-58
Generalized Blow-Up of Corners and Fiber Products....Pages 59-62
Trace Expansions for Elliptic Cone Operators....Pages 63-67
Spectral Geometry for the Riemann Moduli Space....Pages 69-72
Invariant Integral Operators on the Oshima Compactification of a Riemannian Symmetric Space: Kernel Asymptotics and Regularized Traces....Pages 73-76
Pseudodifferential Operators on Manifolds with Foliated Boundaries....Pages 77-80
The Determinant of the Laplacian on a Conically Degenerating Family of Metrics....Pages 81-84
Front Matter....Pages 85-85
Relatively Isospectral Noncompact Surfaces....Pages 87-89
Microlocal Analysis of Scattering Data for Nested Conormal Potentials....Pages 91-94
Front Matter....Pages 85-85
Equidistribution of Eisenstein Series for Convex Co-compact Hyperbolic Manifolds....Pages 95-98
Lower Bounds for the Counting Function of an Integral Operator....Pages 99-102
The Identification Problems in SPECT: Uniqueness, Non-uniqueness and Stability....Pages 103-104
Eigenvalues and Spectral Determinants on Compact Hyperbolic Surfaces....Pages 105-107
Front Matter....Pages 109-109
A Support Theorem for a Nonlinear Radiation Field....Pages 111-112
Propagation of Singularities Around a Lagrangian Submanifold of Radial Points....Pages 113-116
Local Energy Decay for Several Evolution Equations on Asymptotically Euclidean Manifolds....Pages 117-120
Rayleigh Surface Waves and Geometric Pseudo-differential Calculus....Pages 121-124
Topological Implications of Global Hypoellipticity....Pages 125-127
Chern-Simons Line Bundle on Teichm?ller Space....Pages 129-132
A Simple Diffractive Boundary Value Problem on an Asymptotically Anti-de Sitter Space....Pages 133-136
Quantization in a Magnetic Field....Pages 137-144
Price’s Law on Black Hole Space-Times....Pages 145-148

---

Microlocal analysis is a mathematical field that was invented for the detailed investigation of problems from partial differential equations in the mid-20th century and that incorporated and elaborated on many ideas that had originated in physics. Since then, it has grown to a powerful machine used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. This book collects extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the University of T?bingen from June 14th to 18th, 2011.
Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Local Smoothing with a Prescribed Loss for the Schr?dinger Equation....Pages 3-6
Propagation Through Trapped Sets and Semiclassical Resolvent Estimates....Pages 7-10
Space–Adiabatic Theory for Random–Landau Hamiltonian: Results and Prospects....Pages 11-14
Microlocal Analysis of FIOs with Singularities....Pages 15-17
A Nonlinear Adiabatic Theorem for Coherent States....Pages 19-23
Adiabatic Limits and Related Lattice Point Problems....Pages 25-28
The Effective Hamiltonian in Curved Quantum Waveguides and When It Does Not Work....Pages 29-32
The Adiabatic Limit of the Laplacian on Thin Fibre Bundles....Pages 33-36
Adiabatic Limit with Isolated Degenerate Fibres....Pages 37-43
Microlocal Analysis and Adiabatic Problems: The Case of Perturbed Periodic Schr?dinger Operators....Pages 45-48
Recent Results in Semiclassical Approximation with Rough Potentials....Pages 49-52
Front Matter....Pages 53-53
On the Closure of Elliptic Wedge Operators....Pages 55-58
Generalized Blow-Up of Corners and Fiber Products....Pages 59-62
Trace Expansions for Elliptic Cone Operators....Pages 63-67
Spectral Geometry for the Riemann Moduli Space....Pages 69-72
Invariant Integral Operators on the Oshima Compactification of a Riemannian Symmetric Space: Kernel Asymptotics and Regularized Traces....Pages 73-76
Pseudodifferential Operators on Manifolds with Foliated Boundaries....Pages 77-80
The Determinant of the Laplacian on a Conically Degenerating Family of Metrics....Pages 81-84
Front Matter....Pages 85-85
Relatively Isospectral Noncompact Surfaces....Pages 87-89
Microlocal Analysis of Scattering Data for Nested Conormal Potentials....Pages 91-94
Front Matter....Pages 85-85
Equidistribution of Eisenstein Series for Convex Co-compact Hyperbolic Manifolds....Pages 95-98
Lower Bounds for the Counting Function of an Integral Operator....Pages 99-102
The Identification Problems in SPECT: Uniqueness, Non-uniqueness and Stability....Pages 103-104
Eigenvalues and Spectral Determinants on Compact Hyperbolic Surfaces....Pages 105-107
Front Matter....Pages 109-109
A Support Theorem for a Nonlinear Radiation Field....Pages 111-112
Propagation of Singularities Around a Lagrangian Submanifold of Radial Points....Pages 113-116
Local Energy Decay for Several Evolution Equations on Asymptotically Euclidean Manifolds....Pages 117-120
Rayleigh Surface Waves and Geometric Pseudo-differential Calculus....Pages 121-124
Topological Implications of Global Hypoellipticity....Pages 125-127
Chern-Simons Line Bundle on Teichm?ller Space....Pages 129-132
A Simple Diffractive Boundary Value Problem on an Asymptotically Anti-de Sitter Space....Pages 133-136
Quantization in a Magnetic Field....Pages 137-144
Price’s Law on Black Hole Space-Times....Pages 145-148
....