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arXiv · 1804.10055

Tight frames and related geometric problems

Grigory Ivanov
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Abstract

We study the properties of a set of vectors called tight frames that obtained as the orthogonal projection of some orthonormal basis of $\R^n$ onto $\R^k.$ 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.

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Grigory Ivanov. 2018-04-25. Tight frames and related geometric problems. https://doi.org/10.4153/s000843952000096x

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