Asymptotics for Christoffel functions associated to continuum Schrödinger operators

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.