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A Discrete Leading Symbol and Spectral Asymptotics for Natural Differential Operators

✍ Scribed by Ivan Avramidi; Thomas Branson

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 296 KB
Volume: 190
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2001.3886

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✦ Synopsis

We initiate a systematic study of natural differential operators in Riemannian geometry whose leading symbols are not of Laplace type. In particular, we define a discrete leading symbol for such operators which may be computed pointwise, or from spectral asymptotics. We indicate how this can be applied to the computation of another kind of spectral asymptotics, namely asymptotic expansions of fundamental solutions, and to the computation of conformally covariant operators.

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