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.