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

DOI:
https://doi.org/10.1090/S0002-9947-97-01846-1

MathSciNet review:
1401772

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Abstract | References | Similar Articles | Additional Information

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

Email:
harrell@math.gatech.edu

**Joachim Stubbe II**

Affiliation:
Département de Physique Théorique, Université de Genève, Geneva, Switzerland

Email:
stubbe@cernvm.cern.ch

DOI:
https://doi.org/10.1090/S0002-9947-97-01846-1

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