On the higher-dimensional wavelet frames. (Q1421496)

A frame multiresolution analysis \(\{V_n, \phi\}\) as introduced by Benedetto and Li is a tool for construction of wavelet frames for \(L^2(\mathbb R^d)\): the definition of a FMRA corresponds to the definition of an MRA, except that the translates \(\{T_k\phi\}\) are required to form a frame for \(V_0\) instead of an ONB. This yields extra freedom in the achievable constructions. In the present paper, frames in \(L^2(\mathbb R^d), d>1\), are constructed via a FMRA, combined with a splitting trick on \(V_1\) and a partition of \(\mathbb R^d\). In contrast to the \(1-D\) case, several generators are needed; the minimal number is characterized.