The Laplace Transform in the Study of Equations with Infinitely Many Derivatives

摘要

We implement afunctional calculus via Laplace transform in order to solve linear equations of the form f(l_t)0 = J(t) , t ≥ 0 , in which f is an entire function. Furthermore we analyze the delicate issue of the formulation of initial value problems for nonlocal equations such as (1).