arXiv Analytics

Sign in

arXiv:1408.7111 [math.AP]AbstractReferencesReviewsResources

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

Abel Klein, C. S. Sidney Tsang

Published 2014-08-29Version 1

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.

Comments: 14 pages
Categories: math.AP
Subjects: 35B99, 81Q10
Related articles: Most relevant | Search more
arXiv:2103.05531 [math.AP] (Published 2021-03-09)
Pointwise Weyl Laws for Schrödinger operators with singular potentials
arXiv:1506.07431 [math.AP] (Published 2015-06-24)
Manifold decompositions and indices of Schrödinger operators
arXiv:1301.2460 [math.AP] (Published 2013-01-11, updated 2013-08-04)
On unique continuation for Schrödinger operators of fractional and higher orders

Links

Toolbox