Analytic Representations of Sequences in $L^p$ Spaces, $1\leq p<\infty$


Vesna Manova Erakovi\'k, Stevan Pilipović, Vasko Rečkovski




In this paper we consider a sequence of functions in $L^p(\mathbb R)$, $1\leq p<\infty$ 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.