Finite tight frames are interesting in various topics including questions of quantum information. Each complex frame leads to a resolution the identity Hilbert space. Symmetric informationally complete measurements special class equiangular frames. Applications such physics deserve more attention than they have obtained. We derive uncertainty relations for measurement assigned an frame. Main re...

Recent results from real algebraic geometry and the theory of polynomial optimization are related in a new framework to the existence question of multivariate tight wavelet frames whose generators have at least one vanishing moment. Namely, several equivalent formulations of the so-called Unitary Extension Principle (UEP) from [33] are interpreted in terms of hermitian sums of squares of certai...

A Grassmannian frame is a collection of unit vectors which are optimally incoherent. The most accessible (and perhaps most beautiful) of Grassmannian frames are equiangular tight frames (ETFs); indeed, there are infinite families of known ETFs, whereas only finitely many non-ETF Grassmannian frames are known to date. This paper surveys every known construction of ETFs and tabulates existence fo...

Spectral tetris is a flexible and elementary method to derive unit norm frames with a given frame operator having all of its eigenvalues ≥ 2. One important application of this method is to construct fusion frames. We will give necessary and sufficient conditions for a spectral tetris construction to give a fusion frame with prescribed eigenvalues for its fusion frame operator and with prescribe...