To date, frames have established themselves as a standard notion in applied mathematics,
computer science, and engineering as a means to derive redundant, yet stable …

" The early chapters contain the topics from linear algebra that students need to know in
order to read the rest of the book. The later chapters are devoted to advanced topics, which …

We investigate the optimal configurations of n points on the unit sphere for a class of
potential functions. In particular, we characterize these optimal configurations in terms of …

Finite unit norm tight frames provide Parseval-like decompositions of vectors in terms of
redundant components of equal weight. They are known to be robust against additive noise …

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 …

We study the harmonic analysis of Bernoulli measures μ λ, a one-parameter family of
compactly supported Borel probability measures on the real line. The parameter λ is a fixed …

Scalable frames are frames with the property that the frame vectors can be rescaled
resulting in tight frames. However, if a frame is not scalable, one has to aim for an …

This paper studies the frames corresponding to oversampled filter banks (FBs). For this class
of FB frames, we present a state-space parameterization of perfect reconstruction FB frames …

Given a finite sequence of vectors 𝓕 0 \mathcalF_0 in ℂ d we describe the spectral and
geometrical structure of optimal frame completions of 𝓕 0 \mathcalF_0 obtained by …

In this paper we characterize and construct novel oversampled filter banks implementing
fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum …