The resolvent parametrix of the general elliptic linear differential operator: a closed form for the intrinsic symbol

Abstract

Nonrecursive, explicit expressions are obtained for the term of arbitrary order in the asymptotic expansion of the intrinsic symbol of a resolvent parametrix of an elliptic linear differential operator, of arbitrary order and algebraic structure, which acts on sections of a vector bundle over a manifold. Results for the conventional symbol are included as a special case.