Geodesic
Tight frames and related geometric problems
Canadian mathematical bulletin, Tome 64 (2021) no. 4, pp. 942-963

Voir la notice de l'article provenant de la source Cambridge

DOI

A tight frame is the orthogonal projection of some orthonormal basis of $\mathbb {R}^n$ onto $\mathbb {R}^k.$ 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 condition for local extrema of these problems. As applications, we prove new results for the problem of maximization of the volume of zonotopes.
DOI : 10.4153/S000843952000096X
Mots-clés : Tight frame, Grassmannian, zonotope, volume 
Ivanov, Grigory. Tight frames and related geometric problems. Canadian mathematical bulletin, Tome 64 (2021) no. 4, pp. 942-963. doi: 10.4153/S000843952000096X
@article{10_4153_S000843952000096X,
     author = {Ivanov, Grigory},
     title = {Tight frames and related geometric problems},
     journal = {Canadian mathematical bulletin},
     pages = {942--963},
     year = {2021},
     volume = {64},
     number = {4},
     doi = {10.4153/S000843952000096X},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S000843952000096X/}
}
TY  - JOUR
AU  - Ivanov, Grigory
TI  - Tight frames and related geometric problems
JO  - Canadian mathematical bulletin
PY  - 2021
SP  - 942
EP  - 963
VL  - 64
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S000843952000096X/
DO  - 10.4153/S000843952000096X
ID  - 10_4153_S000843952000096X
ER  - 
%0 Journal Article
%A Ivanov, Grigory
%T Tight frames and related geometric problems
%J Canadian mathematical bulletin
%D 2021
%P 942-963
%V 64
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/S000843952000096X/
%R 10.4153/S000843952000096X
%F 10_4153_S000843952000096X

Cité par Sources :