Full Spark Frames in the Orbit of a Representation
Representation Theory
2020-05-19 v2 Functional Analysis
Abstract
We present a new infinite family of full spark frames in finite dimensions arising from a unitary group representation, where the underlying group is the semi-direct product of a cyclic group by a group of automorphisms. The only previously known algebraically constructed infinite families were the harmonic, Gabor and Dihedral frames. Our construction hinges on a theorem that requires no group structure. Additionally, we illustrate our results by providing explicit constructions of full spark frames.
Cite
@article{arxiv.1909.06223,
title = {Full Spark Frames in the Orbit of a Representation},
author = {Romanos Diogenes Malikiosis and Vignon Oussa},
journal= {arXiv preprint arXiv:1909.06223},
year = {2020}
}
Comments
25 pages; incorporated referees' remarks