Pseudodifferential Operators and Their Fredholm Properties

Abstract

Pseudodifferential operators are a natural extension of linear integral and partial differential operators. The theory of such operators grew out of the study of singular integral operators by Giraud, Mikhlin, Calderón and Zygmund, among others. It developed rapidly after 1965 with the systematic studies of Kohn and Nirenberg [114], Hörmander, and other researchers. This theory has found many fields of application. In particular, all the boundary integral operators corresponding to the elliptic boundary value problems studied in this book are such operators. By using such a theory, the analysis of boundary integral equations and boundary element methods can be either greatly simplified or presented in a more general and elegant form.