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Geometric conditions for the exact controllability of fractional free and harmonic Schrödinger equations

We provide necessary and sufficient geometric conditions for the exact controllability of the one-dimensional fractional free and fractional harmonic Schrödinger equations. The necessary and sufficient condition for the exact controllability of fractional free Schrödinger equations is derived from the Logvinenko-Sereda theorem and its quantitative version established by Kovrijkine, whereas the one for the exact controllability of fractional harmonic Schrödinger equations is deduced from an infinite dimensional version of the Hautus test for Hermite functions and the Plancherel-Rotach formula.

preprint2020arXivOpen access
Jérémy MartinKarel Pravda-Starov
math.AP
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Open access2 authors1 topic
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Jérémy MartinKarel Pravda-Starov

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