Universal series in ∩ _{p >1} ℓ ^p

Abstract

In this paper an abstract condition is given yielding universal series defined by sequences a = {a j } ∞ j=1 in ∩p>1 p but not in 1 . We obtain a unification of some known results related to approximation by translates of specific functions including the Riemann ζ-function, or a fundamental solution of a given elliptic operator in R ν with constant coefficients or an approximate identity as, for example, the normal distribution. Another application gives universal trigonometric series in R ν simultaneously with respect to all σ-finite Borel measures in R ν . Stronger results are obtained by using universal Dirichlet series.