" 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 characterize the existence of finite tight frames whose frame elements are of
predetermined length. In particular, we derive a “fundamental inequality” which completely …

Let $\mathcal H $ be a Hilbert space. Given a bounded positive definite operator $ S $ on
$\mathcal H $, and a bounded sequence $\mathbf {c}=\{c_k\} _ {k\in\mathbb N} $ of …

We develop a natural generalization of vector-valued frame theory, which we term operator-
valued frame theory, using operator-algebraic methods. This extends work of the second …

When constructing finite frames for a given application, the most important consideration is
the spectrum of the frame operator. Indeed, the minimum and maximum eigenvalues of the …

The objective of this paper is to improve the customary definition of redundancy by providing
quantitative measures in its place, which we coin upper and lower redundancies, that match …

We consider the space F^ E_ {k, n} of all spherical tight frames of k vectors in real or complex
n--dimensional Hilbert space E^ n, ie E= R or E= C, and its orbit space G^ E_ {k, n}= F^ E …

This chapter is an introduction to an open conjecture in time-frequency analysis on the linear
independence of a finite set of time-frequency shifts of a given L 2 function. Background and …

Fusion frame theory is an emerging mathematical theory that provides a natural framework
for performing hierarchical data processing. A fusion frame can be regarded as a frame-like …

Abstract The (μ, S)-frames are frames with lengths in μ 1⋅⋅⋅ μ N and with frame operator S,
or the F=f_1⋯f_N∈M_d*N(E) with column lengths listed by μ and which satisfy FF∗= S. In …