Quasi-orthogonal decompositions of structured frames

A decomposition of a Hilbert space H into a quasi-orthogonal family of closed subspaces is introduced. We shall investigate conditions in order to derive bounded families of corresponding quasi-projectors or resolutions of the identity operator. Given a local family of atoms, or generalized stable basis, for each subspace; we show that the union of the local atoms can generate a global frame for the Hilbert space. Corresponding duals can be calculated in a flexible way by means of systems of quasi-projectors. An application to Gabor frames is presented as example of the use of this technique, for calculation of duals and explicit estimates of lattice constants. (C) 2003 Elsevier Inc. All rights reserved.