Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a desired fusion frame operator and dimensions for subspaces, one existing method for creating unitweight fusion frames with these properties is the flexible a...

The relevance in sampling theory of U -invariant subspaces of a Hilbert space H, where U denotes a unitary operator on H, is nowadays a recognized fact. Indeed, shift-invariant subspaces of L(R) become a particular example; periodic extensions of finite signals provide also a remarkable example. As a consequence, the availability of an abstract U -sampling theory becomes a useful tool to handle...

The deepest and most difficult question in Fusion Frame Theory is the construction of fusion frames with added properties for specific applications. In frame theory we have a powerful tool introduced by Benedetto and Fickus [1] called frame potentials (See [5] for a deep analysis of frame potentials). Frame potentials are a valuable tool for showing the existence of frames with certain specifie...

In this note some necessary or/and sufficient conditions for the perturbation of a (Ω, μ)-frame are given. We also discussed (Ω, μ)-frames of subspaces.

Sensorineural systems often use groups of redundant neurons to represent stimulus information both during transduction and population coding of features. This redundancy makes the system more robust to corruption in the representation. We approximate neural coding as a projection of the stimulus onto a set of vectors, with the result encoded by spike trains. We use the formalism of frame theory...

A new paradigm in sampling theory has been developed recently by Lu and Do. In this new approach the classical linear model is replaced by a non-linear, but structured model consisting of a union of subspaces. This is the natural approach for the new theory of compressed sampling, representation of sparse signals and signals with finite rate of innovation. In this article we extend the theory o...

We study some equivalency relations between Hilbert frames and closed subspaces of l2(I). We define also a distance between frames and we establish the geometric meaning of this metric. Finally we find the closest and respectively the nearest tight frame to a given frame.