A Note on the Wodzicki Residue

Abstract

In this note we explain the relationship of the Wodzicki residue of (certain powers of) an elliptic differential operator $P$\ acting on sections of a complex vector bundle $E$\ over a closed compact manifold $M$\ and the asymptotic expansion of the trace of the corresponding heat operator $e^{-tP}$. In the special case of a generalized laplacian $△$\ and $\dim M>2$, we thereby obtain a simple proof of the fact already shown in [KW], that the Wodzicki residue $res({△}^{-\frac{n}{2}+1})$\ is the integral of the second coefficient of the heat kernel expansion of $△$\ up to a proportional factor.

3 pages, plain tex replaced with 9606006