The Resolvent of an Elliptic Boundary Problem

Abstract

This paper and its successor, [10], extend to boundary value problems the analysis of the powers of an elliptic operator given in [9]. (Similar methods are applied in [3], [5], and [6] for the case without boundary; [5a] announces boundary results.) Although [9] treated general elliptic pseudo-differential operators on compact manifolds, we restrict ourselves here to differential operators, except in the final section, where we correct some (fortunately inconsequential) errors in the proof given in [9]. We consider a q X q system A = > aaDa of Cdifferential operators