Frames of periodic shift-invariant spaces (Q5929847)

Equivalent conditions for a family \(\Phi=\{\varphi_k\}_{k\in N}\) to generate a frame for a shift-invariant subspace of \(L^2([0,1]^s)\) are given; the characterization is in terms of some operators defined on \(\ell^2\) via the bracket product on \(L^2([0,1]^s)\). Also the case where \(\Phi\) is a frame for all of \(L^2([0,1]^s)\) is characterized.