Abstract
In this paper, we investigate trace expansions of operatorsof the form Aη(tL) where η: R→C is a Schwartz function, A and L are classical pseudo-differential operators on a compact manifold M with L elliptic. In particular, we show that, under certain hypotheses,this trace admits an expansion in powers of t→0+. We also relate the constant coefficient to the non-commutative residue and the canonical trace of A. Our main tool is the continuous inclusion of the functional calculus of L into the pseudo-differential calculus whose proof relies on the Helffer-Sjöstrand formula.
Original language | English |
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Pages (from-to) | 2159-2202 |
Number of pages | 44 |
Journal | Documenta Mathematica |
Volume | 24 |
DOIs | |
Publication status | Published - 2019 |
Keywords
- Canonical trace
- Non-commutative residues
- Pseudodifferential operators on manifolds
ASJC Scopus subject areas
- General Mathematics