García García, AntonioHernández Medina, Miguel ÁngelPérez Villalón, Gerardo2021-04-232021-04-232020-02-05Results in Mathematics, (2020), v. 75, Article number: 40.1422-6383https://hdl.handle.net/10016/32474A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space H is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group G on H. The samples are defined by means of a filtering process which generalizes the usual sampling settings. The multiply generated setting allows to consider some examples where the group G is non-abelian as, for instance, crystallographic groups. Finally, it is worth to mention that classical average or pointwise sampling in shift-invariant subspaces are particular examples included in the followed approach.22eng© 2020 Springer Nature Switzerland AG.Convolution systemsDiscrete abelian groupsDual framesSampling expansionUnitary representation of a groupresearch articleMatemáticashttps://doi.org/10.1007/s00025-020-1164-yopen access122Results in Mathematics75AR/0000025589