Two-channel sampling in wavelet subspaces

We develop two-channel sampling theory in the wavelet subspace V₁ from the multi resolution analysis {V_j}_j∈𝕫. Extending earlier results by G. G. Walter [11], W. Chen and S. Itoh [2] and Y. M. Hong et al [5] on the sampling theory in the wavelet or shift invariant spaces, we find a necessary and sufficient condition for two-channel sampling expansion formula to hold in V₁.