---
_id: '13128'
abstract:
- lang: eng
text: "Given A⊆GL2(Fq), we prove that there exist disjoint subsets B,C⊆A such
that A=B⊔C and their additive and multiplicative energies satisfying max{E+(B),E×(C)}≪|A|3/M(|A|),
where\r\nM(|A|)=min{q4/3/|A|1/3(log|A|)2/3,|A|4/5/q13/5(log|A|)27/10}.\r\n We
also study some related questions on moderate expanders over matrix rings, namely,
for A,B,C⊆GL2(Fq), we have |AB+C|, |(A+B)C|≫q4, whenever |A||B||C|≫q10+1/2.
These improve earlier results due to Karabulut, Koh, Pham, Shen, and Vinh ([2019],
Expanding phenomena over matrix rings, ForumMath., 31, 951–970).\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ali
full_name: Mohammadi, Ali
last_name: Mohammadi
- first_name: Thang
full_name: Pham, Thang
last_name: Pham
- first_name: Yiting
full_name: Wang, Yiting
id: 1917d194-076e-11ed-97cd-837255f88785
last_name: Wang
orcid: 0000-0002-2856-767X
citation:
ama: Mohammadi A, Pham T, Wang Y. An energy decomposition theorem for matrices and
related questions. Canadian Mathematical Bulletin. 2023;66(4):1280-1295.
doi:10.4153/S000843952300036X
apa: Mohammadi, A., Pham, T., & Wang, Y. (2023). An energy decomposition theorem
for matrices and related questions. Canadian Mathematical Bulletin. Cambridge
University Press. https://doi.org/10.4153/S000843952300036X
chicago: Mohammadi, Ali, Thang Pham, and Yiting Wang. “An Energy Decomposition Theorem
for Matrices and Related Questions.” Canadian Mathematical Bulletin. Cambridge
University Press, 2023. https://doi.org/10.4153/S000843952300036X.
ieee: A. Mohammadi, T. Pham, and Y. Wang, “An energy decomposition theorem for matrices
and related questions,” Canadian Mathematical Bulletin, vol. 66, no. 4.
Cambridge University Press, pp. 1280–1295, 2023.
ista: Mohammadi A, Pham T, Wang Y. 2023. An energy decomposition theorem for matrices
and related questions. Canadian Mathematical Bulletin. 66(4), 1280–1295.
mla: Mohammadi, Ali, et al. “An Energy Decomposition Theorem for Matrices and Related
Questions.” Canadian Mathematical Bulletin, vol. 66, no. 4, Cambridge University
Press, 2023, pp. 1280–95, doi:10.4153/S000843952300036X.
short: A. Mohammadi, T. Pham, Y. Wang, Canadian Mathematical Bulletin 66 (2023)
1280–1295.
date_created: 2023-06-11T22:00:40Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-29T11:00:46Z
day: '01'
department:
- _id: GradSch
doi: 10.4153/S000843952300036X
external_id:
arxiv:
- '2106.07328'
isi:
- '001011963000001'
intvolume: ' 66'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2106.07328
month: '12'
oa: 1
oa_version: Preprint
page: 1280-1295
publication: Canadian Mathematical Bulletin
publication_identifier:
eissn:
- 1496-4287
issn:
- 0008-4395
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: An energy decomposition theorem for matrices and related questions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 66
year: '2023'
...
---
_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. Canadian Mathematical
Bulletin. 2021;64(4):942-963. doi:10.4153/s000843952000096x
apa: Ivanov, G. (2021). Tight frames and related geometric problems. Canadian
Mathematical Bulletin. Canadian Mathematical Society. https://doi.org/10.4153/s000843952000096x
chicago: Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” Canadian
Mathematical Bulletin. Canadian Mathematical Society, 2021. https://doi.org/10.4153/s000843952000096x.
ieee: G. Ivanov, “Tight frames and related geometric problems,” Canadian Mathematical
Bulletin, 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.” Canadian
Mathematical Bulletin, vol. 64, no. 4, Canadian Mathematical Society, 2021,
pp. 942–63, doi:10.4153/s000843952000096x.
short: G. Ivanov, Canadian Mathematical Bulletin 64 (2021) 942–963.
date_created: 2022-03-18T09:55:59Z
date_published: 2021-12-18T00:00:00Z
date_updated: 2023-09-05T12:43:09Z
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'
...