Abstract For t∈{1, 2,…} fixed, a natural class of spherical designs is given by the vectors v
1,…, vn in F d= R d, C d (not all zero) which give equality in the bound∑ j= 1 n∑ k= 1 n|< vj …

Two decades ago, Zauner conjectured that for every dimension d, there exists an
equiangular tight frame consisting of d 2 vectors in C d. Most progress to date explicitly …

Frames provide redundant, stable representations of data which have important applications
in signal processing. We introduce a connection between symplectic geometry and frame …

We consider the following questions: when do there exist quaternionic frames with given
frame spectrum and given frame vector norms? When such frames exist, is it always …

The collection of d× N complex matrices with prescribed column norms and singular values
forms an algebraic variety, which we refer to as a frame space. Elements of frame spaces …

We introduce a projective Riesz s-kernel for the unit sphere S^ d-1 S d-1 and investigate
properties of N-point energy minimizing configurations for such a kernel. We show that these …

We introduce an extension to local principal component analysis for learning symmetric
manifolds. In particular, we use a spectral method to approximate the Lie algebra …

Normal matrices, or matrices which commute with their adjoints, are of fundamental
importance in pure and applied mathematics. In this paper, we study a natural functional on …

Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in
signal processing. There has been much recent work on understanding the global structure …

Motivated from two decades old famous Feichtinger conjectures for frames, $ R_\varepsilon
$-conjecture and Weaver's conjecture for Hilbert spaces (and their solution by Marcus …