SAMPLING EXPANSION IN SHIFT INVARIANT SPACES

摘要

For any φ(t) in L{sup}2(R), let V (φ) be the closed shift invariant subspace of L{sup}2(R) spanned by integer translates {φ(t-n) : n ∈ Z} of φ(t). Assuming that φ(t) is a frame or a Riesz generator of V (φ), we first find conditions under which V (φ) becomes a reproducing kernel Hilbert space. We then find necessary and sufficient conditions under which an irregular or a regular shifted sampling expansion formula holds on V (φ) and obtain truncation error estimates of the sampling series. We also find a sufficient condition for a function in L{sup}2(R) that belongs to a sampling subspace of L{sup}2(R). Several illustrating examples are also provided.