Real Trace Expansions

  • Véronique Fischer

    Department of Mathematical Sciences, University of Bath, BA2 7AY Bath, UK
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In this paper, we investigate trace expansions of operators of the form Aη(tL)A\eta(t\mathcal{L}) where η:RC\eta:\mathbb{R}\rightarrow\mathbb{C} is a Schwartz function, AA and L\mathcal L are classical pseudo-differential operators on a compact manifold MM with L\mathcal L elliptic. In particular, we show that, under certain hypotheses, this trace admits an expansion in powers of t0+t\rightarrow 0^+. We also relate the constant coefficient to the non-commutative residue and the canonical trace of AA. Our main tool is the continuous inclusion of the functional calculus of L\mathcal{L} into the pseudo-differential calculus whose proof relies on the Helffer-Sjöstrand formula.

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Véronique Fischer, Real Trace Expansions. Doc. Math. 24 (2019), pp. 2159–2202

DOI 10.4171/DM/723