Asymptotics for Christoffel functions associated to continuum Schrödinger operators

Eichinger, Benjamin (2024) Asymptotics for Christoffel functions associated to continuum Schrödinger operators. Journal d'Analyse Mathématique, 153 (2). pp. 519-553. ISSN 0021-7670

Abstract

We prove asymptotics of the Christoffel function, λL(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 LλL(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 λL(ξ), we compute universality limits for continuum Schrödinger operators at scale L and obtain clock spacing of the eigenvalues of the finite range truncations.