Ebook: Microlocal Analysis and Spectral Theory
- Tags: Partial Differential Equations, Global Analysis and Analysis on Manifolds, Quantum Physics, Operator Theory, Integral Transforms Operational Calculus
- Series: NATO ASI Series 490
- Year: 1997
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
The NATO Advanced Study Institute "Microlocal Analysis and Spectral The ory" was held in Tuscany (Italy) at Castelvecchio Pascoli, in the district of Lucca, hosted by the international vacation center "11 Ciocco" , from September 23 to October 3, 1996. The Institute recorded the considerable progress realized recently in the field of Microlocal Analysis. In a broad sense, Microlocal Analysis is the modern version of the classical Fourier technique in solving partial differential equa tions, where now the localization proceeding takes place with respect to the dual variables too. Precisely, through the tools of pseudo-differential operators, wave-front sets and Fourier integral operators, the general theory of the lin ear partial differential equations is now reaching a mature form, in the frame of Schwartz distributions or other generalized functions. At the same time, Microlocal Analysis has grown up into a definite and independent part of Math ematical Analysis, with other applications all around Mathematics and Physics, one major theme being Spectral Theory for Schrodinger equation in Quantum Mechanics.
Content:
Front Matter....Pages i-viii
Linear Partial Differential Equations with Multiple Involutive Characteristics....Pages 1-38
Gevrey and Analytic Hypoellipticity....Pages 39-59
Higher Microlocalization and Propagation of Singularities....Pages 61-90
Conormality and Lagrangian Properties in Diffractive Boundary Value Problems....Pages 91-113
Parametrized Pseudodifferential Operators and Geometric Invariants....Pages 115-164
Boundary Value Problems and Edge Pseudo-Differential Operators....Pages 165-226
Wodzicki’s Noncommutative Residue and Traces for Operator Algebras on Manifolds with Conicai Singularities....Pages 227-250
Lower Bounds for Pseudodifferential Operators....Pages 251-262
Weyl Formula for Globally Hypoelliptic Operators in Rn ....Pages 263-306
Splitting in Large Dimension and Infrared Estimates....Pages 307-347
Microlocal Exponential Estimates and Applications to Tunneling....Pages 349-376
A Trace Formula and Review of Some Estimates for Resonances....Pages 377-437
Back Matter....Pages 439-444
Content:
Front Matter....Pages i-viii
Linear Partial Differential Equations with Multiple Involutive Characteristics....Pages 1-38
Gevrey and Analytic Hypoellipticity....Pages 39-59
Higher Microlocalization and Propagation of Singularities....Pages 61-90
Conormality and Lagrangian Properties in Diffractive Boundary Value Problems....Pages 91-113
Parametrized Pseudodifferential Operators and Geometric Invariants....Pages 115-164
Boundary Value Problems and Edge Pseudo-Differential Operators....Pages 165-226
Wodzicki’s Noncommutative Residue and Traces for Operator Algebras on Manifolds with Conicai Singularities....Pages 227-250
Lower Bounds for Pseudodifferential Operators....Pages 251-262
Weyl Formula for Globally Hypoelliptic Operators in Rn ....Pages 263-306
Splitting in Large Dimension and Infrared Estimates....Pages 307-347
Microlocal Exponential Estimates and Applications to Tunneling....Pages 349-376
A Trace Formula and Review of Some Estimates for Resonances....Pages 377-437
Back Matter....Pages 439-444
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