On the noncommutative residue and the heat trace expansion on conic manifolds

Juan B. Gil, Paul A. Loya

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)309-327
Number of pages19
JournalManuscripta Mathematica
Volume109
Issue number3
DOIs
StatePublished - Dec 1 2002

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Heat
Trace
Cone
Pseudodifferential Operators
Resolvent
Argand diagram
Asymptotic Expansion
Differential operator
Algebra
Coefficient
Term
Operator

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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On the noncommutative residue and the heat trace expansion on conic manifolds. / Gil, Juan B.; Loya, Paul A.

In: Manuscripta Mathematica, Vol. 109, No. 3, 01.12.2002, p. 309-327.

Research output: Contribution to journalArticle

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