GEOMETRIC CONDITIONS FOR THE EXACT CONTROLLABILITY OF FRACTIONAL FREE AND HARMONIC SCHRÖDINGER EQUATIONS

Jérémy Martin , Karel Pravda-Starov (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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 controllabil-ity of fractional harmonic Schrödinger equations is deduced from an infinite dimensional version of the Hautus test for Hermite functions and the Plancherel-Rotach formula.

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Jérémy Martin, Karel Pravda-Starov. GEOMETRIC CONDITIONS FOR THE EXACT CONTROLLABILITY OF FRACTIONAL FREE AND HARMONIC SCHRÖDINGER EQUATIONS. Journal of Evolution Equations, 2021, 21 (1), pp.1059-1087. ⟨10.1007/s00028-020-00618-6⟩. ⟨hal-02893885⟩