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Title: Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators
Authors: Biswas, Anup
Lorinczi, Jozsef
Issue Date: 2017
Publisher: arXiv
Citation: BISWAS, A. and LORINCZI, J., 2017. Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators. arXiv:1710.11596, 29pp.
Abstract: We derive a lower bound on the location of global extrema of eigenfunctions for a large class of non-local Schrödinger operators in convex domains under Dirichlet exterior conditions, featuring the symbol of the kinetic term, the strength of the potential, and the corresponding eigenvalue, and involving a new universal constant. We show a number of probabilistic and spectral geometric implications, and derive a Faber-Krahn type inequality for non-local operators. Our study also extends to potentials with compact support, and we establish bounds on the location of extrema relative to the boundary edge of the support or level sets around minima of the potential.
Description: This is a arXiv pre-print.
Version: Submitted for publication
URI: https://dspace.lboro.ac.uk/2134/27630
Publisher Link: https://arxiv.org/abs/1710.11596
Appears in Collections:Pre-prints (Maths)

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