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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Asymptotics for Christoffel functions associated to continuum Schrödinger operators
AU - Eichinger, Benjamin
PY - 2024/9/1
Y1 - 2024/9/1
N2 - 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.
AB - 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.
U2 - 10.1007/s11854-023-0319-7
DO - 10.1007/s11854-023-0319-7
M3 - Journal article
VL - 153
SP - 519
EP - 553
JO - Journal d'Analyse Mathématique
JF - Journal d'Analyse Mathématique
SN - 0021-7670
IS - 2
ER -