Commutator bounds for eigenvalues,with applications to spectralgeometry |
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| Authors: | Evans M. Harrell II Patricia L. Michel |
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| Affiliation: | Center for Dynamical Systems and Nonlinear Studies School of Mathematics , Georgia Institute of Technology , Atlanta , 30332-0160 , Georgia E-mail: harrell@math.gatech.edu |
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| Abstract: | We prove a purely algebraic version of an eigenvalue inequality of Hile and Protter, and derive corollaries bounding differences of eigenvalues of Laplace– Beltrami operators on manifolds. We significantly improve earlier bounds of Yang and Yau, Li, and Harrell. |
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| Keywords: | Elliptic regularity Parabolic regularity Invariant measure Sub-Markovian semigroup Singular diffusion AMS 1991 Subject Classification: Primary: 35J15, 35K10, 60J35, Secondary: 35D10, 35B65, 60J60, 35R05 |
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