Some asymptotic formulas for elliptic pseudodifferential operators (Q1094596)

Let M be a smooth closed n-dimensional manifold and A be a classical pseudo-differential operator on M with the principal symbol \(a_ 0\). Suppose that the values of \(a_ 0\) lie in \({\mathbb{C}}\setminus L\), where L is a closed non-empty angle in the complex plane with the vertex in the origin. The author obtains the complete asymptotic expansion in L for the function K(x,x,\(\xi)\) where K(x,y,\(\xi)\) is the kernel of the operator \((A-\xi I)^{-1}\).