### 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 language | English (US) |
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Pages (from-to) | 309-327 |

Number of pages | 19 |

Journal | Manuscripta Mathematica |

Volume | 109 |

Issue number | 3 |

DOIs | |

State | Published - Dec 1 2002 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Manuscripta Mathematica*,

*109*(3), 309-327. https://doi.org/10.1007/s00229-002-0308-6

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*Manuscripta Mathematica*, vol. 109, no. 3, pp. 309-327. https://doi.org/10.1007/s00229-002-0308-6

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the noncommutative residue and the heat trace expansion on conic manifolds

AU - Gil, Juan B.

AU - Loya, Paul A.

PY - 2002/12/1

Y1 - 2002/12/1

N2 - 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.

AB - 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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UR - http://www.scopus.com/inward/citedby.url?scp=0036027237&partnerID=8YFLogxK

U2 - 10.1007/s00229-002-0308-6

DO - 10.1007/s00229-002-0308-6

M3 - Article

AN - SCOPUS:0036027237

VL - 109

SP - 309

EP - 327

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 3

ER -