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

Alexander Dicke (), Albrecht Seelmann () and Ivan Veselić ()
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Alexander Dicke: Technische Universität Dortmund
Albrecht Seelmann: Technische Universität Dortmund
Ivan Veselić: Technische Universität Dortmund

Partial Differential Equations and Applications, 2024, vol. 5, issue 2, 1-18

Abstract: 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 $$L^2$$ L 2 -estimates and an $$H^1$$ H 1 -concentration estimate, all of them for functions in a spectral subspace of the operator.

Keywords: Spectral inequalities; Uncertainty relation; Schroedinger operator; Shubin operator; Decay of eigenfunctions; Confinement potential; Observability; Primary 35Pxx; Secondary 35J10; 35B40 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s42985-024-00276-0

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