 
Summary: ON APPROXIMATIONS BY SHIFTS OF THE
GAUSSIAN FUNCTION.
GERARD ASCENSI
Abstract. The paper study the discrete sets of translations of
the Gaussian function that span the spaces L1
(R) and L2
(R).
1. Introduction.
The study of the sets of translations of functions that span Lp
(R)
spaces is a classical topic in harmonic analysis. One wants to determine
under what conditions a sequence {(t  ) span these spaces for a
function Lp
(R) and a set R. Wiener's Tauberian theorem [17]
asserts that {(t  )}R span L2
(R) if and only if the set of points
at which the Fourier transform of vanishes has measure 0, and span
L1
(R) if this set is empty. It is natural to consider this problem when
is a discrete set. We give an overview of the results on this topic in
