Geodesic
Real Trace Expansions
Documenta mathematica, Tome 24 (2019), pp. 2159-2202
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In this paper, we investigate trace expansions of operators of 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.
DOI : 10.4171/dm/723
Classification : 58J40, 58J42
Mots-clés : pseudodifferential operators on manifolds, non-commutative residues, canonical trace 
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     author = {V\'eronique Fischer},
     title = {Real {Trace} {Expansions}},
     journal = {Documenta mathematica},
     pages = {2159--2202},
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     volume = {24},
     doi = {10.4171/dm/723},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/723/}
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Véronique Fischer. Real Trace Expansions. Documenta mathematica, Tome 24 (2019), pp. 2159-2202. doi: 10.4171/dm/723

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