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Full asymptotic expansion of the heat trace for non–self–adjoint elliptic cone operators
Author(s) -
Gil Juan B.
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310020
Subject(s) - parametrix , mathematics , trace (psycholinguistics) , resolvent , elliptic operator , differential operator , gravitational singularity , asymptotic expansion , mathematical analysis , cone (formal languages) , operator (biology) , semi elliptic operator , manifold (fluid mechanics) , conical surface , pure mathematics , heat kernel , geometry , chemistry , mechanical engineering , linguistics , philosophy , biochemistry , repressor , transcription factor , engineering , gene , algorithm
The operator e – tA and its trace Tr e – tA , for t > 0, are investigated in the case when A is an elliptic differential operator on a manifold with conical singularities. Under a certain spectral condition (parameter–ellipticity) we obtain a full asymptotic expansion in t of the heat trace as t → 0 + . As in the smooth compact case, the problem is reduced to the investigation of the resolvent ( A – λ ) –1 . The main step consists in approximating this family by a parametrix of A – λ constructed within a suitable parameter–dependent calculus.