Approximation by Multiinteger Translates of Functions Having Global Support Original Research Article

We consider Lp-approximation (1 ≤ p ≤ ∞) by multiinteger translates of several functions which are not necessarily compactly supported but have a suitable decay rate. In particular, we introduce a modified notion of controlled approximation and characterize the controlled approximation order in terms of the Strang-Fix conditions.