Pseudodifferential operator techniques

Author: None
Publisher:
Publish Date: 2000-06-01
Features: It is generally well known that the Fourier-Laplace transform converts a linear constant coefficient PDE P(D)u = f on R^n to an equation P(σ)u - σ = f - σ, for the transforms u, f of u and f, so that solving P(D)u = f just amounts to division by the polynomial P(σ). The practical application was suspect and ill understood, however, until the theory of distributions provided a basis for a logically consistent theory. Thereafter it became the Fourier-Laplace method for solving initial-boundary problems for standard PDEs. We recall these facts in some detail in secs. 1-4 of ch. 0. This book is in English.
Introduction: 1. Introductory discussions; 2. Calculus of pseudodifferential operators; 3. Elliptic operators and parametrices in R^n, etc.