Error estimates for irregular sampling of band-limited functions on a locally compact Abelian group

Abstract

Band-limited functions f can be recovered from their sampling values ( f( x i )) by means of iterative methods, if only the sampling density is high enough. We present an error analysis for these methods, treating the typical forms of errors, i.e., jitter error, truncation error, aliasing error, quantization error, and their combinations. The derived apply uniformly to whole families of spaces, e.g., to weighted L p -spaces over some locally compact Abelian group with growth rate up to some given order. In contrast to earlier papers we do not make use of any (relative) separation condition on the sampling sets. Furthermore we discard the assumption on polynomial growth of the weights that has been used over Euclidean spaces. Consequently, even for the case of regular sampling, i.e., sampling along lattices in G, the results are new in the given generality.