Microlocal Analysis and Spectral Theory

✍ Scribed by O. Liess, L. Rodino (auth.), Luigi Rodino (eds.)

• Publisher: Springer Netherlands
• Year: 1997
• Tongue: English
• Leaves: 448
• Series: NATO ASI Series 490
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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 R n ....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

✦ Subjects

Partial Differential Equations;Global Analysis and Analysis on Manifolds;Quantum Physics;Operator Theory;Integral Transforms, Operational Calculus