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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A coefficient of an asymptotic expansion
of logarithms of determinants
for classical elliptic
pseudodifferential operators with parameters


Author: Yoonweon Lee
Journal: Proc. Amer. Math. Soc. 124 (1996), 3885-3888
MSC (1991): Primary 58G15, 58G26
MathSciNet review: 1317041
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Abstract: For classical elliptic pseudodifferential operators $A(\lambda )$ of order $m>0$ with parameter $\lambda $ of weight $\chi >0$, it is known that $\log \det_\theta A(\lambda )$ admits an asymptotic expansion as $\lambda \to+\infty $. In this paper we show, with some assumptions, that the coefficient of $\lambda ^{-1/\chi }$ can be expressed by the value of a zeta function at 0 for some elliptic $\psi \operatorname{DO}$ on $M\times S^1$ multiplied by $\frac {m}{2}$.


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Additional Information

Yoonweon Lee
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Address at time of publication: Department of Mathematics, College of Natural Science, Inha University, 253 Yonghyun-dong, Nam-gu, Inchon, Korea 402-751
Email: ywonlee@dragon.inha.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03268-6
PII: S 0002-9939(96)03268-6
Received by editor(s): September 6, 1994
Received by editor(s) in revised form: December 12, 1994
Communicated by: Peter Li
Article copyright: © Copyright 1996 American Mathematical Society