---
_id: '10860'
abstract:
- lang: eng
  text: A tight frame is the orthogonal projection of some orthonormal basis of Rn
    onto Rk. 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 condition for local extrema
    of these problems. As applications, we prove new results for the problem of maximization
    of the volume of zonotopes.
acknowledgement: The author was supported by the Swiss National Science Foundation
  grant 200021_179133. The author acknowledges the financial support from the Ministry
  of Education and Science of the Russian Federation in the framework of MegaGrant
  no. 075-15-2019-1926.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Grigory
  full_name: Ivanov, Grigory
  id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
  last_name: Ivanov
citation:
  ama: Ivanov G. Tight frames and related geometric problems. <i>Canadian Mathematical
    Bulletin</i>. 2021;64(4):942-963. doi:<a href="https://doi.org/10.4153/s000843952000096x">10.4153/s000843952000096x</a>
  apa: Ivanov, G. (2021). Tight frames and related geometric problems. <i>Canadian
    Mathematical Bulletin</i>. Canadian Mathematical Society. <a href="https://doi.org/10.4153/s000843952000096x">https://doi.org/10.4153/s000843952000096x</a>
  chicago: Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” <i>Canadian
    Mathematical Bulletin</i>. Canadian Mathematical Society, 2021. <a href="https://doi.org/10.4153/s000843952000096x">https://doi.org/10.4153/s000843952000096x</a>.
  ieee: G. Ivanov, “Tight frames and related geometric problems,” <i>Canadian Mathematical
    Bulletin</i>, vol. 64, no. 4. Canadian Mathematical Society, pp. 942–963, 2021.
  ista: Ivanov G. 2021. Tight frames and related geometric problems. Canadian Mathematical
    Bulletin. 64(4), 942–963.
  mla: Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” <i>Canadian
    Mathematical Bulletin</i>, vol. 64, no. 4, Canadian Mathematical Society, 2021,
    pp. 942–63, doi:<a href="https://doi.org/10.4153/s000843952000096x">10.4153/s000843952000096x</a>.
  short: G. Ivanov, Canadian Mathematical Bulletin 64 (2021) 942–963.
corr_author: '1'
date_created: 2022-03-18T09:55:59Z
date_published: 2021-12-18T00:00:00Z
date_updated: 2024-10-09T21:01:50Z
day: '18'
department:
- _id: UlWa
doi: 10.4153/s000843952000096x
external_id:
  arxiv:
  - '1804.10055'
  isi:
  - '000730165300021'
intvolume: '        64'
isi: 1
issue: '4'
keyword:
- General Mathematics
- Tight frame
- Grassmannian
- zonotope
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1804.10055
month: '12'
oa: 1
oa_version: Preprint
page: 942-963
publication: Canadian Mathematical Bulletin
publication_identifier:
  eissn:
  - 1496-4287
  issn:
  - 0008-4395
publication_status: published
publisher: Canadian Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tight frames and related geometric problems
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 64
year: '2021'
...