Asymptotics for Christoffel functions associated to continuum Schrödinger operators

2022/04/12 by Benjamin Eichinger, Eichinger, Benjamin · 1 citation
Computer Science · Mathematics · #31C35 #34L20 #34L40 #47B32 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2204.05633

openalex publication_date 2022/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove asymptotics of the Christoffel function, λ_L(ξ), of a continuum Schrödinger operator for points in the interior of the essential spectrum under some mild conditions on the spectral measure. It is shown that Lλ_L(ξ) has a limit and that this limit is given by the Radon--Nikodym derivative of the spectral measure with respect to the Martin measure. Combining this with a recently developed local criterion for universality limits at scale λ_L(ξ), we compute universality limits for continuum Schrödinger operators at scale L and obtain clock spacing of the eigenvalues of the finite range truncations.

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