UNCERTAINTY PRINCIPLES IN GELFAND-SHILOV SPACES AND NULL-CONTROLLABILITY

Jérémy Martin (1, 2)

1 UR Mathématiques - Université de Rennes - UFR Mathématiques
2 IRMAR - Institut de Recherche Mathématique de Rennes

We provide new uncertainty principles for functions in a general class of Gelfand-Shilov spaces. These results apply, in particular, with the classical Gelfand-Shilov spaces as well as for spaces of functions with weighted Hermite expansions. Thanks to these uncertainty principles, we derive null-controllability results for evolution equations with adjoint systems enjoying smoothing effects in specific Gelfand-Shilov spaces. More precisely, we consider control subsets which are thick with respect to a quasi linearly growing density and establish sufficient conditions on the growth of the density to ensure null-controllability of these evolution equations.

Mots clés: Uncertainty principles; observability; Gelfand-Shilov spaces

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Jérémy Martin. UNCERTAINTY PRINCIPLES IN GELFAND-SHILOV SPACES AND NULL-CONTROLLABILITY. Journal of Functional Analysis, 2022, 283 (9), pp.article n° 109619. ⟨10.1016/j.jfa.2022.109619⟩. ⟨hal-03463849⟩