Quantitative unique continuation for spectral subspaces of Schr\"odinger operators with singular potentials
Analysis of PDEs
2023-07-12 v2 Mathematical Physics
Functional Analysis
math.MP
Spectral Theory
Abstract
Recent (scale-free) quantitative unique continuation estimates for spectral subspaces of Schr\"odinger operators are extended to allow singular potentials such as certain -functions. The proof is based on accordingly adapted Carleman estimates. Applications include Wegner and initial length scale estimates for random Schr\"odinger operators and control theory for the controlled heat equation with singular heat generation term.
Cite
@article{arxiv.2011.01801,
title = {Quantitative unique continuation for spectral subspaces of Schr\"odinger operators with singular potentials},
author = {Alexander Dicke and Christian Rose and Albrecht Seelmann and Martin Tautenhahn},
journal= {arXiv preprint arXiv:2011.01801},
year = {2023}
}
Comments
18 pages; updated references, some typos fixed, minor editorial changes