Grubb G. Functional Calculus of Pseudo-Differential Boundary Problems

Birkhäuser Boston, 1986. - 511 Pages.Pseudo differential methods are central to the study of partial differential equations, because they permit an 'algebraization', a replacement of compositions of operators in n-space by simpler product rules for their symbols. The main purpose of this book is to set up an operational calculus for operators defined from differential and pseudodifferential boundary value problems via a resolvent construction. A secondary purpose is to give a complete treatment of the properties of the calculus of pseudodifferential boundary problems with transmission, both the first version by Boutet de Monvel and in a global version, as well as in versions containing a parameter running in an unbounded set. And finally, the book presents some applications to evolution problems, fractional powers, index theory, spectral theory and singular perturbation theory.