MULTI-CHANNEL SAMPLING ON SHIFT-INVARIANT SPACES WITH FRAME GENERATORS

摘要

Let Φ be a continuous function in L~2(R) such that the sequence {Φ(t - n)}_(n∈Z) is a frame sequence in L~2(R) and assume that the shift-invariant space V (Φ) generated by has a multi-banded spectrum σ(V). The main aim in this paper is to derive a multichannel sampling theory for the shift-invariant space V(Φ). By using a type of Fourier duality between the spaces V(Φ) and L~2[0, 2π] we find necessary and sufficient conditions allowing us to obtain stable multi-channel sampling expansions in V(Φ).