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Geometric Conditions for the Exact Observability of Schr\"{o}dinger Equations with Point Interaction and Inverse-Square Potentials on Half-Line
Authors
Zhiwen Duan
Longben Wei
Hui Xu
Publication date
25 July 2023
Publisher
View
on
arXiv
Abstract
We provide necessary and sufficient conditions for the exact observability of the Schrodinger equations with point interaction and inverse-square potentials on half-line. The necessary and sufficient condition for these two cases are derived from two Logvinenko-Sereda type theorems for generalized Fourier transform. Specifically, the generalized Fourier transform associated to the Schr\"{o}dinger operators with inverse-square potentials on half-line are the well known Hankel transforms. We provide a necessary and sufficient condition for a subset
Ω
\Omega
Ω
such that a function with its Hankel transform supporting in a given interval can be bounded, in
L
2
L^{2}
L
2
-norm, from above by its restriction to the set
Ω
\Omega
Ω
, with constant independent of the position of the intervalComment: arXiv admin note: text overlap with arXiv:2003.11263, arXiv:2007.04096 by other author
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oai:arXiv.org:2307.09592
Last time updated on 26/07/2023