In this paper, we investigate trace expansions of operators of the form where is a Schwartz function, and are classical pseudo-differential operators on a compact manifold with elliptic. In particular, we show that, under certain hypotheses, this trace admits an expansion in powers of . We also relate the constant coefficient to the non-commutative residue and the canonical trace of . Our main tool is the continuous inclusion of the functional calculus of into the pseudo-differential calculus whose proof relies on the Helffer-Sjöstrand formula.
Cite this article
Véronique Fischer, Real Trace Expansions. Doc. Math. 24 (2019), pp. 2159–2202DOI 10.4171/DM/723