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

Abstract

We prove a spectral inequality (a specific type of uncertainty relation) for Schrödinger operators with confinement potentials, in particular of Shubin-type. The sensor sets are allowed to decay exponentially, where the precise allowed decay rate depends on the potential. The proof uses an interpolation inequality derived by Carleman estimates, quantitative weighted $L^2$-estimates and an $H^1$-concentration estimate, all of them for functions in a spectral subspace of the operator.

17 pages; fixed typos, and editorial changes

References in corpus (4)

• An abstract Logvinenko-Sereda type theorem for spectral subspaces
• Uncertainty principle for Hermite functions and null-controllability with sensor sets of decaying density
• Uncertainty principles with error term in Gelfand-Shilov spaces
• Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials

Cited by in corpus (1)

• Unique continuation estimates for Baouendi--Grushin equations on cylinders