Linear Partial Differential Operators in Gevrey Spaces

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