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arXiv · 1810.01931

Real trace expansions

Veronique Fischer
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Abstract

In this paper, we show that the trace of the operators $A\eta(t\mathcal{L})$ 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 $t\to 0^+$. The functions $\eta$ 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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Veronique Fischer. 2018-10-03. Real trace expansions. https://arxiv.org/abs/1810.01931

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