Properties of oblique dual frames in shift-invariant systems

Gramian analysis is used to study properties of a shift-invariant system , where B is an invertible n×n matrix and Φ a finite or countable subset of L2(Rn) under the assumption that the system forms a frame for the closed subspace M of L2(Rn). In particular, the relationship between various features of such system, such as being a frame for the whole space L2(Rn), being a Riesz sequence and having a unique shift-generated dual of type I or II is discussed in details. Several interesting examples are presented.