An Inverse Problem for LTV ODE’s

Abstract

It is well known that any linear combination of products of polynomials and exponentials (a.k.a. Bohl functions) are annihilated by LTI-ODE’s. In this paper, we consider the more general classes of piecewise Bohl functions and of real analytic functions and present the realization of the latter as solutions of linear differential polynomials with real analytic coefficients. In particular, we show that the minimal order depends solely on the multiplicity of the zeros of the given function. We extend the problem further to meromorphic functions without poles on the real line. We briefly comment on piecewise-defined functions and the nonhomogeneous problem.