Abstract
AbstractWe 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 $$L^2$$
L
2
-estimates and an $$H^1$$
H
1
-concentration estimate, all of them for functions in a spectral subspace of the operator.
Funder
Technische Universität Dortmund
Publisher
Springer Science and Business Media LLC
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