One-Sided and Two-Sided Green´s Functions$^1$

We discuss the one-sided Green's function, associated with an initial value problem and the two-sided Green's function related to a boundary value problem. We present an especific calculation associated with a differential equation with constant coefficients. For both problems we present also the Laplace integral transform as another methodology to calculate these Green functions, and conclude which is the most convinient. An incursion in the so-called fractional Green's function is also presented. As an example we discuss the isotropic harmonic oscillator.