Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials

Abstract

Recent (scale-free) quantitative unique continuation estimates for spectral subspaces of Schrödinger operators are extended to allow singular potentials such as certain $L^p$-functions. The proof is based on accordingly adapted Carleman estimates. Applications include Wegner and initial length scale estimates for random Schrödinger operators and control theory for the controlled heat equation with singular heat generation term.

18 pages; updated references, some typos fixed, minor editorial changes

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Cited by in corpus (1)

• Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials