Sampling for shift-invariant and wavelet subspaces

We investigate several issues surrounding the general question of when a function in a finitely generated shift invariant subspace of L-2(R) can be determined by certain of its sample values just as a function bandlimited to [-1/2, 1/2] can be expressed in terms of its integer samples. The main theme here is how answers to this question depend on general properties of the generators of the shift invariant space, such as orthogonality properties, scaling relations, smoothness and so forth. One of the main issues that Re address is the question of how to control aliasing error.