- 95-431 Harrell Evans M. II, Stubbe Joachim
- On Trace Identities and Universal Eigenvalue Estimates for Some Partial Differential Operators
Sep 24, 95
(auto. generated ps),
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Abstract. In this article, we prove and exploit a trace identity for the spectra of
Schr\"odinger 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.