On almost periodic sequences

A sequence u = (u(n)) of complex numbers is said to be algebraic (differentially finite) if the generating power series [GRAPHICS] is algebraic over C(z) (satisfy a linear differential equation with polynomial coefficients). In this note, we study such sequences that belongs to the space of almost periodic sequences, i .e. the completion of the space spanned by the sequences c(theta)(n) = theta(n), theta is an element of U = {z is an element of C; \z\ = 1} under the semi-norm [GRAPHICS]