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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
DOI: https://doi.org/10.1090/S0002-9939-96-03268-6
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 $\frac {m}{2}$.


References [Enhancements On Off] (What's this?)

  • [BFK] D. Burghelea, L. Friedlander, and T. Kappeler, Mayer-Vietoris type formula for determinants of elliptic differential operators, J. Funct. Anal. 107 (1992), 34-65. MR 93f:58242
  • [Se] R. Seeley, Complex powers of an elliptic operator, Proc. Sympos. Pure Math., vol. 10, Amer. Math. Soc., Providence, RI, 1967, pp. 288-307. MR 38:6220
  • [Sh] M. A. Shubin, Pseudodifferential operators and spectral theory, Springer-Verlag, Berlin and New York, 1985.
  • [Wo] M. Wodzicki, Spectral asymmetry and zeta functions, Invent. Math. 66 (1982), 115-135. MR 83h:58097

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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: https://doi.org/10.1090/S0002-9939-96-03268-6
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

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