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- W2884761566 abstract "We characterize the potential-energy functions $V(x)$ that minimize the gap $Gamma$ between the two lowest Sturm-Liouville eigenvalues for [ H(p,V) u := -frac{d}{dx} left(p(x)frac{du}{dx}right)+V(x) u = lambda u, quadquad xin [0,pi ], ] where separated self-adjoint boundary conditions are imposed at end points, and $V$ is subject to various assumptions, especially convexity or having a form. In the classic case where $p=1$ we recover with different arguments the result of Lavine that $Gamma$ is uniquely minimized among convex $V$ by the constant, and in the case of single-well potentials, with no restrictions on the position of the minimum, we obtain a new, sharp bound, that $Gamma > 2.04575dots$." @default.
- W2884761566 created "2018-08-03" @default.
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- W2884761566 date "2018-07-22" @default.
- W2884761566 modified "2023-09-27" @default.
- W2884761566 title "Optimal bounds on the fundamental spectral gap with single-well potentials" @default.
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