Luigi Rodino

The book is devoted to new and classical results of the theory of linear partial differential operators in Gevrey spaces. The ?microlocal approach? is adopted, by using pseudo-differential operators, wave front sets and Fourier integral operators.Basic results for Schwartz-distributions, cì and analytic classes are also included, concerning hypoellipticity, solvability and propagation of singularities.Also included is a self-contained exposition of the calculus of the pseudo-differential operators of infinite order.

Linear Partial Differential Operators in Gevrey Spaces

Fabio Nicola

This book presents a global pseudo-differential calculus in Euclidean spaces, which includes SG as well as Shubin classes and their natural generalizations containing Schroedinger operators with non-polynomial potentials. This calculus is applied to study global hypoellipticity for several pseudo-differential operators. The book includes classic calculus as a special case. It will be accessible to graduate students and of benefit to researchers in PDEs and mathematical physics.

Global Pseudo-differential Calculus on Euclidean Spaces

M. W. Wong

This volume consists of peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held on August 13-18, 2007, and invited papers by experts in the field.

ISAAC Group in Pseudo-Differential Operators (IGPDO), Middle East Technical University, Ankara,Turkey, August 2007

New Developments in Pseudo-Differential Operators

Lamberto Cattabriga

CONTENTS: J.M. Bony: Analyse microlocale des equations aux derivees partielles non lineaires.- G.G. Grubb: Parabolic pseudo-differential boundary problems and applications.- L. H|rmander: Quadratic hyperbolic operators.- H. Komatsu: Microlocal analysis in Gevrey classes and in complex domains.- J. Sj|strand: Microlocal analysis for the periodic magnetic Schr|dinger equation and related questions.

Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Montecatini Terme, Italy, July 3-11, 1989

Microlocal Analysis and Applications

Bert-Wolfgang Schulze

Man Wah Wong

This volume is based on lectures given at the workshop on pseudo-differential operators held at the Fields Institute from December 11, 2006 to December 15, 2006. The two main themes of the workshop and hence this volume are partial differential equations and time-frequency analysis. The contents of this volume consist of five mini-courses for graduate students and post-docs, and fifteen papers on related topics. Of particular interest in this volume are the mathematical underpinnings, applications and ramifications of the relatively new Stockwell transform, which is a hybrid of the Gabor transform and the wavelet transform. The twenty papers in this volume reflect modern trends in the development of pseudo-differential operators.

Partial Differential Equations and Time-frequency Analysis

Pseudo-differential Operators

The book is devoted to new and classical results of the theory of linear partial differential operators in Gevrey spaces. The “microlocal approach” is adopted, by using pseudo-differential operators, wave front sets and Fourier integral operators. Basic results for Schwartz-distributions, c∞ and analytic classes are also included, concerning hypoellipticity, solvability and propagation of singularities. Also included is a self-contained exposition of the calculus of the pseudo-differential operators of infinite order. Contents:IntroductionGevrey Functions and UltradistributionsBasic Problems and Basic Operators in Gevrey ClassesPseudo-Differential OperatorsOperators with Multiple Characteristics Readership: Mathematicians. keywords:Mathematics;Mathematical Analysis;Partial Differential Equations;Pseudo-Differential Equations;Microlocal Analysis;Function Spaces;Gevrey Spaces;Hypoellipticity;Local Solvability;Multiple Characteristics “The book is well written, reasonably self-contained, gives a number of examples, and has an adequate bibliography.” SIAM Review “The book is a good introduction to the Gevrey microlocal analysis for students and post-graduate students, but it is also useful for all specialists working in the domain of the general theory of linear partial differential operators.” Mathematics Abstracts

Luigi Rodino

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