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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On trace identities and
universal eigenvalue estimates for
some partial differential operators

Authors: Evans M. Harrell II and Joachim Stubbe II
Journal: Trans. Amer. Math. Soc. 349 (1997), 1797-1809
MSC (1991): Primary 35J10, 35J25, 58G25
MathSciNet review: 1401772
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Abstract: In this article, we prove and exploit a trace identity for the spectra of Schrödinger operators and similar operators. This identity leads to universal bounds on the spectra, which apply to low-lying eigenvalues, eigenvalue asymptotics, and to partition functions (traces of heat operators). In many cases they are sharp in the sense that there are specific examples for which the inequalities are saturated. Special cases corresponding to known inequalities include those of Hile and Protter and of Yang.

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Additional Information

Evans M. Harrell II
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160

Joachim Stubbe II
Affiliation: Département de Physique Théorique, Université de Genève, Geneva, Switzerland

Keywords: Schr\"{o}dinger operator, eigenvalue gap, trace, heat kernel, partition function
Received by editor(s): September 28, 1995
Additional Notes: The first author was supported in part by US NSF Grant DMS 9211624.
Article copyright: © Copyright 1997 American Mathematical Society