A corona theorem for an algebra of Radon measures with an application to exact controllability for linear controlled delayed difference equations

Abstract

This paper proves a corona theorem for the algebra of Radon measures compactly supported in ${\mathbb{R}}_{-}$ and this result is applied to provide a necessary and sufficient Hautus--type frequency criterion for the $L^1$ exact controllability of linear controlled delayed difference equations (LCDDE). Hereby, it solves an open question raised in [6].