Error estimates for irregular sampling of band-limited functions on a locally compact abelian group
The authors study various types of error estimates for certain reconstruction methods. These results extend the corresponding earlier results given for the Euclidean \(n\)-space only. Also, these error estimates apply uniformly to large families of function spaces. These results are new even for the case of regular sampling over locally compact Abelian groups, i.e., for the case that the sampling values are taken from some lattice in this group (a discrete subgroup with compact quotient). They give qualitative estimates for the jitter error, for the aliasing error, or truncation errors and combined errors.
scientific article; zbMATH DE number 1915757