Uncertainty principles in Gelfand-Shilov spaces and null-controllability

TL;DR

This paper establishes new uncertainty principles in Gelfand-Shilov spaces and applies them to prove null-controllability of certain evolution equations with smoothing effects.

Contribution

It introduces novel uncertainty principles for Gelfand-Shilov spaces and links these to null-controllability results for evolution equations with specific smoothing properties.

Findings

New uncertainty principles for Gelfand-Shilov spaces

Null-controllability results for evolution equations with smoothing effects

Control subsets characterized by thick sets with growth conditions

Abstract

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.