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

This paper proves a corona theorem for the algebra of Radon measures compactly supported in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℝ</mml:mi> <mml:mo>-</mml:mo> </mml:msub> </mml:math> and this result is applied to provide a necessary and sufficient Hautus–type frequency criterion for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> exact controllability of linear controlled delayed difference equations (LCDDE). Hereby, it solves an open question raised in [5].