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Sampling expansion formula in shift-invariant spaces

Let ￠(t) be a square integrable function on the real line such that its integer translates {￠( t - k) : k ∈ ?} forms a frame sequence or a Riesz sequence. Let V(￠) be the shift invariant space in L²(?), which is generated by ￠(t). We first find conditions under which V(￠) becomes a reproducing kernel Hilbert space. We then develop general sampling theory on V(￠) including both irregular and regular sampling either via a frame or a Riesz basis expansion, which unifies and extends some previous results on the same topic by many authors.