Asymptotics for Christoffel functions associated to continuum Schrödinger operators

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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