Frames consisting of translates of a single function play an important role in sampling theory as well as in wavelet theory and Gabor analysis. We give a necessary and sufficient condition for a subfamily of regularly spaced translates of a function φ ∈ L(R), (τnbφ)n∈Λ, Λ ⊂ Z, to form a frame (resp. Riesz basis) for its closed linear span. One consequence is that if Λ ⊂ N , then this family is ...

Democratic systems arise in the context of greedy approximations in Banach spaces. The greedy algorithm is an important method in numerical mathematics; for more details see the early work of V. N. Temlyakov [16], [17]. At the same time it also points to some interesting issues in functional analysis. In particular, we would like to emphasize the basic theorem of S. V. Konyagin and V. N. Temlya...