On trace identities and universal eigenvalue estimates for some partial differential operators
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- by Evans M. Harrell II and Joachim Stubbe PDF
- Trans. Amer. Math. Soc. 349 (1997), 1797-1809 Request permission
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.References
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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
- Affiliation: Département de Physique Théorique, Université de Genève, Geneva, Switzerland
- Email: stubbe@cernvm.cern.ch
- Received by editor(s): September 28, 1995
- Additional Notes: The first author was supported in part by US NSF Grant DMS 9211624.
- © Copyright 1997 American Mathematical Society
- 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