一维单阱Robin Schr dinger算子的谱隙
Spectral gaps of 1-D Robin Schrödinger operators with single-well potentials
摘要：
我们证明了清晰的下界的频谱间隙的1维薛定谔算子的罗宾边界条件的罗宾参数的每个值。特别是，我们的下界适用于单阱势与中心过渡点。这一结果将Cheng等人和Horváth在Neumann和Dirichlet端点情形下的工作推广到插值情形。我们还建立在最近的工作由安德鲁斯，Clutterbuck，和Hauer的情况下，凸和对称的单阱势。特别地，我们证明了对称势的谱隙是Robin参数的增函数。
英文摘要：
We prove sharp lower bounds on the spectral gap of 1-dimensional Schrödinger operators with Robin boundary conditions for each value of the Robin parameter. In particular, our lower bounds apply to single-well potentials with a centered transition point. This result extends work of Cheng et al. and Horváth in the Neumann and Dirichlet endpoint cases to the interpolating regime. We also build on recent work by Andrews, Clutterbuck, and Hauer in the case of convex and symmetric single-well potentials. In particular, we show the spectral gap is an increasing function of the Robin parameter for symmetric potentials.
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