Abstract
We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary p-groups (Zp)d, we introduce an averaging procedure that leads to a natural object of study: a 4-tuple of functions which can be regarded as a common generalization of tiles and spectral sets. We characterize such 4-tuples for d = 1, 2, and prove some partial results for d = 3.