On the Noncommutative Residue and the Heat Trace Expansion on Conic Manifolds

Details On the Noncommutative Residue and the Heat Trace Expansion on Conic Manifolds On the Noncommutative Residue and the Heat Trace Expansion on Conic Manifolds

2001-09-21

arxiv.org/abs/math/0109154v1

Mathematics

Spectral Theory

15 pages

Scientific paper

Given a cone pseudodifferential operator $P$ we give a full asymptotic expansion as $t\to 0^+$ of the trace $\Tr Pe^{-tA}$, where $A$ is an elliptic cone differential operator for which the resolvent exists on a suitable region of the complex plane. Our expansion contains $\log t$ and new $(\log t)^2$ terms whose coefficients are given explicitly by means of residue traces. Cone operators are contained in some natural algebras of pseudodifferential operators on which unique trace functionals can be defined. As a consequence of our explicit heat trace expansion, we recover all these trace functionals.

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