Lyapunov exponents for linear delay equations in arbitrary phase spaces (Q2494138)

The author presents results on the asymptotics of the solution of an inhomogeneous linear delay differential equation with infinite delay. Rather than fixing a particular state space, he follows the usual axiomatic approach, i.e., the state space is a normed linear space of functions from the negative real line to \({\mathbb C}^d\) satisfying certain hypotheses. Using a state space decomposition like in the monograph of Hale and Verduyn Lunel in the case of finite delays, he studies the exponential growth rates of the solutions. Finally, the case of an equation with additive white noise is treated.