Analytic Representations of Sequences in Lp Spaces, 1 ≤ p < ∞

Abstract

In this paper we consider a sequence of functions in Lp(R), 1 ≤ p < ∞and, in the second part, we
include a sequence of real analytic functions without real roots. We obtain several results regarding their
convergence or the convergence of the sequence of their analytic representations. We, also, give results
about the analytic representation of the product of the boundary functions and other additional results.