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

摘要

Let ϕ be a continuous function in L2(R) such that the sequence {ϕ(t − n)}n∈Z is anframe sequence in L2(R) and assume that the shift-invariant space V (ϕ) generated bynϕ has a multi-banded spectrum σ(V ). The main aim in this paper is to derive a multichannelnsampling theory for the shift-invariant space V (ϕ). By using a type of Fouriernduality between the spaces V (ϕ) and L2[0, 2π] we find necessary and sufficient conditionsnallowing us to obtain stable multi-channel sampling expansions in V (ϕ).