95-431 Harrell Evans M. II, Stubbe Joachim

On Trace Identities and Universal Eigenvalue Estimates for Some Partial Differential Operators (36K, AMSTeX) Sep 24, 95

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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.

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