A geometric estimate on the norm of product of functionals
| dc.creator | Matolcsi, Mate | |
| dc.date | 2006-11-30 | |
| dc.date.accessioned | 2026-07-07T07:33:32Z | |
| dc.date.available | 2026-07-07T07:33:32Z | |
| dc.description | The open problem of determining the exact value of the $n$-th linear polarization constant $c_n$ of $\R^n$ has received considerable attention over the past few years. This paper makes a contribution to the subject by providing a new lower bound on the value of $\sup_{\|{\bf{y}}\|=1}| {\bf{x}}_1,{\bf{y}} ... {\bf{x}}_n,{\bf{y}} |$, where ${\bf{x}}_1, ... ,{\bf{x}}_n$ are unit vectors in $\R^n$. The new estimate is given in terms of the eigenvalues of the Gram matrix $[ {\bf{x}}_i,{\bf{x}}_j ]$ and improves upon earlier estimates of this kind. However, the intriguing conjecture $c_n=n^{n/2}$ remains open. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611947 | |
| dc.identifier | http://arxiv.org/abs/math/0611947 | |
| dc.identifier | Linear Algebra Appl. 405 (2005), 304--310 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119490 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 46G25, 52A40, 46B07 | |
| dc.title | A geometric estimate on the norm of product of functionals | |
| dc.type | text |