Mariano A. Ruiz

Minimization of convex functionals over frame operators

We present results about minimization of convex functionals defined over a finite set of vectors in a finite-dimensional Hilbert space, that extend several known results for the Benedetto-Fickus frame potential. Our approach depends on majorization techniques. We also consider some perturbation problems, where a positive perturbation of the frame operator of a set of vectors is realized as the frame operator of a set of vectors which is close to the original one.

Oblique projections and frames

We characterize those frames on a Hilbert space H which can be represented as the image of an orthonormal basis by an oblique projection defined on an extension K of H. We show that all frames with infinite excess and frame bounds 1 < A < B are of this type. This gives a generalization of a result of Han and Larson which only holds for normalized tight frames.

Nullspaces and frames

In this paper we give new characterizations of Riesz and conditional Riesz frames in terms of the properties of the nullspace of their synthesis operators. On the other hand, we also study the oblique dual frames whose coefficients in the reconstruction formula minimize different weighted norms.

A note on perturbations of fusion frames

In this work, we consider some relationships between a closed range operator

THE SCHUR-HORN THEOREM FOR OPERATORS AND FRAMES WITH PRESCRIBED NORMS AND FRAME OPERATOR.

T

The Structure of Minimizers of the Frame Potential on Fusion Frames

and a fusion frame

Optimal dual frames and frame completions for majorization

\mathcal{W}=(W_i,w_i)_{i\in I}

Some properties of frames of subspaces obtained by operator theory methods

for a Hilbert space

TIGHT FRAME COMPLETIONS WITH PRESCRIBED NORMS.

\mathcal{H}

Optimal frame completions

that provides that the sequence