Local behavior of solutions of the stationary Schr\" odinger equation with singular potentials and bounds on the density of states of Schrödinger operators

We study the local behavior of solutions of the stationary Schr\" od\-inger equation with singular potentials, establishing a local decomposition into a homogeneous harmonic polynomial and a lower order term. Combining a corollary to this result with a quantitative unique continuation principle...

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Bibliographic Details
Published inarXiv.org
Main Authors Klein, Abel, Tsang, C S Sidney
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.08.2014
Subjects
Density of states
Operators (mathematics)
Polynomials
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Summary:We study the local behavior of solutions of the stationary Schr\" od\-inger equation with singular potentials, establishing a local decomposition into a homogeneous harmonic polynomial and a lower order term. Combining a corollary to this result with a quantitative unique continuation principle for singular potentials we obtain log-H\"older continuity for the density of states outer-measure in one, two, and three dimensions for Schr\" odinger operators with singular potentials, results that hold for the density of states measure when it exists.
ISSN:2331-8422