  We prove the existence of sampling sets and interpolation sets near the
critical density, in Paley Wiener spaces of a locally compact abelian (LCA)
group G . This solves a problem left by Gr\"ochenig, Kutyniok, and Seip in the
article: `Landau's density conditions for LCA groups ' (J. of Funct. Anal. 255
(2008) 1831-1850). To achieve this result, we prove the existence of universal
Riesz bases of characters for L2(Omega), provided that the relatively compact
subset Omega of the dual group of G satisfies a multi-tiling condition. This
last result generalizes Fuglede's theorem, and extends to LCA groups setting
recent constructions of Riesz bases of exponentials in bounded sets of Rd.
