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

Abstract

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 φ has a multi-banded spectrum σ(V). The main aim in this paper is to derive a multi-channel 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).