The IO-stability of equations with operators causal with respect to a cone (Q1405943)

The author considers the equation \[ Ax = f\tag{1} \] in the Lebesgue space \(L_p(\mathbb R^n) =L_p(\mathbb R^n,\mathbb C)\). It is assumed that the operator \(A\: L_p(\mathbb R^n) \to L_p(\mathbb R^n)\) is causal. It is proved that the input-output stability [\textit{J. C. Willems}, SIAM J. Control 7, No. 4, 645--671 (1969; Zbl 0186.22001)] of equation (1) is equivalent to the causal invertibility of the operator \(A\).