Abstract
Let φ be a continuous function in L2(ℝ) such that the sequence {φ(t - n)}n∈ℤ is a frame sequence in L2(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 L2[0, 2π] we find necessary and sufficient conditions allowing us to obtain stable multi-channel sampling expansions in V(φ).
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