On trace identities and universal eigenvalue estimates for some partial differential operators |
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Authors: | Evans M Harrell II Joachim Stubbe II |
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Institution: | School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160 ; Département de Physique Théorique, Université de Genève, Geneva, Switzerland |
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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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Keywords: | Schr\"{o}dinger operator eigenvalue gap trace heat kernel partition function |
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