title: Universal series induced by approximate identities and some relevant applications.
abstract: We prove the existence of series [Formula: see text], whose coefficients [Formula: see text] are in [Formula: see text] and whose terms [Formula: see text] are translates by rational vectors in [Formula: see text] of a family of approximations to the identity, having the property that the partial sums are dense in various spaces of functions such as Wiener's algebra [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], for every [Formula: see text], and the space of measurable functions. Applying this theory to particular situations, we establish approximations by such series to solutions of the heat and Laplace equations as well as to probability density functions.
authors.affiliation: Department of Mathematics, University of Athens, 15784 Panepistimiopolis, Greece.
authors.forename: Vassili
authors.initials: V
authors.lastname: Nestoridis
authors.affiliation: Faculty of Mathematics, University of Vienna, 1090 Vienna, Austria.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Schmutzhard
authors.affiliation: Department of Mathematics, University of the Aegean, 83200 Karlovasi, Samos, Greece.
authors.forename: Vangelis
authors.initials: V
authors.lastname: Stefanopoulos
keywords: Approximation to the identity; Gauss kernel; Heat equation; Laplace’s equation; Normal distribution; Poisson kernel; Universal series; Wiener algebra