Quantitative unique continuation principle for Schrödinger operators with singular potentials

DOI10.1090/proc12734zbMath1339.35070arXiv1408.1992OpenAlexW2963669207MaRDI QIDQ2789864

Chi Shing Sidney Tsang, Abel Klein

Publication date: 2 March 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.1992

zbMATH Keywords

spectral projections

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Continuation and prolongation of solutions to PDEs (35B60)

Related Items (11)

Quantitative uniqueness of solutions to second order elliptic equations with singular potentials in two dimensions ⋮ An abstract Logvinenko-Sereda type theorem for spectral subspaces ⋮ Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations ⋮ Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials ⋮ Quantitative unique continuation of solutions to higher order elliptic equations with singular coefficients ⋮ Lower bounds for Dirichlet Laplacians and uncertainty principles ⋮ Local behavior of solutions of the stationary Schrödinger equation with singular potentials and bounds on the density of states of Schrödinger operators ⋮ Quantitative uniqueness of solutions to second-order elliptic equations with singular lower order terms ⋮ The lattice Anderson model with discrete disorder ⋮ Band edge localization beyond regular Floquet eigenvalues ⋮ Localization and eigenvalue statistics for the lattice Anderson model with discrete disorder

Cites Work

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• A comprehensive proof of localization for continuous Anderson models with singular random potentials
• Scale-free unique continuation estimates and applications to random Schrödinger operators
• An optimal Wegner estimate and its application to the global continuity of the integrated density of states for random Schrödinger operators
• On localization in the continuous Anderson-Bernoulli model in higher dimension
• Trudinger type inequalities in $\mathbf {R}^N$ and their best exponents
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