Uncertainty principles in Gelfand-Shilov spaces and null-controllability
Analysis of PDEs
2021-12-06 v1 Optimization and Control
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.
Keywords
Cite
@article{arxiv.2112.01788,
title = {Uncertainty principles in Gelfand-Shilov spaces and null-controllability},
author = {Jérémy Martin},
journal= {arXiv preprint arXiv:2112.01788},
year = {2021}
}