Real trace expansions

2018/10/03 by Fischer, Veronique
#58J40 #58J42 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1810.01931

Abstract

In this paper, we show that the trace of the operators Aη(tL) where A and \mathcal L are classical pseudo-differential operators on a compact manifold M and \mathcal L is elliptic and self-adjoint admits an expansion in powers of t→ 0⁺. The functions η being smooth and compactly supported on \mathbb R have no meromorphic properties, unlike in the case of the heat trace or zeta functions. We also show that the constant coefficients in our expansions are related to the non-commutative residue and the canonical trace of A.

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