Tight frames and related geometric problems
Metric Geometry
2023-06-22 v3 Functional Analysis
Abstract
We study the properties of a set of vectors called tight frames that obtained as the orthogonal projection of some orthonormal basis of onto We show that a set of vectors is a tight frame if and only if the set of all cross products of these vectors is a tight frame. We reformulate a range of problems on the volume of projections (or sections) of regular polytopes in terms of tight frames and write a first-order necessary maximum condition of these problems. As applications, we prove new results for the problem of the maximization of the volume of zonotopes.
Cite
@article{arxiv.1804.10055,
title = {Tight frames and related geometric problems},
author = {Grigory Ivanov},
journal= {arXiv preprint arXiv:1804.10055},
year = {2023}
}