Abstract.
Given a cone pseudodifferential operator P we give a full asymptotic expansion as t → 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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Received: 12 November 2001 / Revised version: 26 June 2002
Mathematics Subject Classification (2000): Primary 58J35; Secondary 35C20, 58J42
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Gil, J., Loya, P. On the noncommutative residue and the heat trace expansion on conic manifolds. Manuscripta Math. 109, 309–327 (2002). https://doi.org/10.1007/s00229-002-0308-6
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DOI: https://doi.org/10.1007/s00229-002-0308-6