Universal Constraints on the Location of Extrema of Eigenfunctions of\n Non-Local Schr "odinger Operators

2017/10/31 by Anup Biswas, Biswas, Anup, József Lőrinczi +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Probability (math.PR) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1710.11596

openalex publication_date 2017/10/31 · openalex created_date 2022/09/07 · openalex updated_date 2026/07/28

Abstract

We derive a lower bound on the location of global extrema of eigenfunctions\nfor a large class of non-local Schr "odinger operators in convex domains under\nDirichlet exterior conditions, featuring the symbol of the kinetic term, the\nstrength of the potential, and the corresponding eigenvalue, and involving a\nnew universal constant. We show a number of probabilistic and spectral\ngeometric implications, and derive a Faber-Krahn type inequality for non-local\noperators. Our study also extends to potentials with compact support, and we\nestablish bounds on the location of extrema relative to the boundary edge of\nthe support or level sets around minima of the potential.\n

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