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ItemOn a transformation of Bohl and its discrete analogue(Georgia Institute of Technology, 2013) Harrell, Evans M. ; Wong, Manwah LilianFritz Gesztesy’s varied and prolific career has produced many transformational contributions to the spectral theory of one-dimensional Schrödinger equations. He has often done this by revisiting the insights of great mathematical analysts of the past, connecting them in new ways, and reinventing them in a thoroughly modern context. In this short note we recall and relate some classic transformations that figure among Fritz Gestesy’s favorite tools of spectral theory, and indeed thereby make connections among some of his favorite scholars of the past, Bohl, Darboux, and Green. After doing this in the context of one-dimensional Schrödinger equations on the line, we obtain some novel analogues for discrete one-dimensional Schrödinger equations.
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ItemSpectra, Geometry and Asymptotics of Some Differential Equations of Mathematical Physics(Georgia Institute of Technology, 2002-06-01) Harrell, Evans M.
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ItemSpectral and asymptotic problems of mathematical physics(Georgia Institute of Technology, 1999) Harrell, Evans M.
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ItemCommutator Bounds for Eigenvalues of Some Differential Operators(Georgia Institute of Technology, 1994-03) Harrell, Evans M. ; Michel, Patricia L.
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ItemCommutator Bounds for Eigenvalues, with Applications to Spectral Geometry(Georgia Institute of Technology, 1994-03) Harrell, Evans M. ; Michel, Patricia L.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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ItemOn the Second Eigenvalue of the Laplace Operator Penalized by Curvature(Georgia Institute of Technology, 1994) Harrell, Evans M.Consider the operator - ∇^2 - q(κ), where - ∇^2 is the (positive) Laplace-Beltrami operator on a closed manifold of the topological type of the two-sphere S^2 and q is a symmetric non-negative quadratic form in the principal curvatures. Generalizing a well-known theorem of J. Hersch for the Laplace-Beltrami operator alone, it is shown in this note that the second eigenvalue λ [1] is uniquely maximized, among manifolds of fixed area, by the true sphere.
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ItemSpectral and variational problems of mathematical physics(Georgia Institute of Technology, 1990) Harrell, Evans M.
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ItemMathematical sciences : operator theory and mathematical physics(Georgia Institute of Technology, 1986) Harrell, Evans M.
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ItemResearch fellowship for Dr. E.M. Harrell(Georgia Institute of Technology, 1984) Harrell, Evans M.