The Kaczmarz algorithm is an iterative method for reconstructing a signal x∈ ℝ d from an
overcomplete collection of linear measurements yn=< x, φ n>, n≥ 1. We prove quantitative …

How can d+ k vectors in ℝ d be arranged so that they are as close to orthogonal as
possible? In particular, define θ (d, k):= min X max x≠ y∈ X|< x, y>| where the minimum is …

Fusion frames enable signal decompositions into weighted linear subspace components.
For positive integers p, we introduce p-fusion frames, a sharpening of the notion of fusion …

In this paper we bring together some of the key ideas and methods of two disparate fields of
mathematical research, frame theory, and optimal transport, using the methods of the …

For a given infinite connected graph G=(V, E) and an arbitrary but fixed conductance
function c, we study an associated graph Laplacian Δ c; it is a generalized difference …

Lower bounds on the maximal cross correlation between vectors in a set were first given by
Welch and then studied by several others. In this work, this is extended to obtaining lower …

The Paley-Wiener Theorem is a classical result about the stability of basis in Banach spaces
claiming that if a sequence is close to a basis, then this sequence is a basis. Similar results …

Using functions from electrical networks (graphs with resistors assigned to edges), we prove
existence (with explicit formulas) of a canonical Parseval frame in the energy Hilbert space …

In this chapter we survey two topics that have recently been investigated in frame theory.
First, we give an overview of the class of scalable frames. These are (finite) frames with the …

We develop a theory of non-uniform sampling in the context of the theory of frames for the
settings of the short time fourier transform and pseudo-differential operators. Our theory is …