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arXiv · 2206.08682

Spectral inequality with sensor sets of decaying density for Schr\"odinger operators with power growth potentials

Alexander Dicke·Albrecht Seelmann·Ivan Veselic
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Abstract

We prove a spectral inequality (a specific type of uncertainty relation) for Schr\"odinger 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.

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Alexander Dicke, Albrecht Seelmann, Ivan Veselic. 2022-06-17. Spectral inequality with sensor sets of decaying density for Schr\"odinger operators with power growth potentials. https://doi.org/10.1007/s42985-024-00276-0

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