Fusion frames are an emerging topic of frame theory, with applications to encoding and distributed sensing. However, little is known about the existence of tight fusion frames. In traditional frame theory, one method for showing that unit norm tight frames exist is to characterize them as the minimizers of an energy functional, known as the frame potential. We generalize the frame potential to ...

In this paper we study the fusion frame potential, that is a generalization of the BenedettoFickus (vectorial) frame potential to the finite-dimensional fusion frame setting. The structure of local and global minimizers of this potential is studied, when we restrict the frame potential to suitable sets of fusion frames. These minimizers are related to tight fusion frames as in the classical vec...

Spectral tetris is a flexible and elementary method to derive unit norm frames with a given frame operator having all of its eigenvalues ≥ 2. One important application of this method is to construct fusion frames. We will give necessary and sufficient conditions for a spectral tetris construction to give a fusion frame with prescribed eigenvalues for its fusion frame operator and with prescribe...

Let {Wi}i∈I be a (redundant) sequence of subspaces each being endowed with a weight vi, and let H be the closed linear span of the Wi’s, a composite Hilbert space. Provided that {(Wi, vi)}i∈I satisfies a certain property which controls the weighted overlaps of the subspaces, it is called a fusion frame. These systems contain conventional frames as a special case, however they go far “beyond fra...

Frames for Hilbert spaces were first introduced by Duffin and Schaeffer [10] in 1952 to study some problems in nonharmonic Fourier series, reintroduced in 1986 by Daubechies, Grossmann and Meyer [8]. Frames are very useful in characterization of function spaces and other fields of applications such as filter bank theory, sigmadelta quantization, signal and image processing and wireless communic...

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...