Simple Approach to Approximation and Dynamical Realization of Pseudodifferential Time Operators Such as Fractional Ones

Abstract

We present a simple approach to the dynamical realization of a wide class of non-rational transfer functions, involving a natural and efficient method with rigorous theoretical background: the so-called diffusive representation. It includes the construction of finite-dimensional approximations for state-space realizations of a wide class of such operators.