Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3667
Articles: 2'599'751
Articles rated: 2609

09 February 2025
 
  » arxiv » 1109.0048

 Article overview



Closure of the cone of sums of 2d-powers in certain weighted $ell_1$-seminorm topologies
Mehdi Ghasemi ; Murray Marshall ; Sven Wagner ;
Date 1 Sep 2011
AbstractBerg, Christensen and Ressel prove that the closure of the cone of sums of squares in the ring of real polynomials in the topology induced by the $ell_1$-norm is equal to the cone consisting of all polynomials which are non-negative on the hypercube $[-1,1]^n$. The result is deduced as a corollary of a general result which is valid for any commutative semigroup. In later work Berg and Maserick and also Berg, Christensen and Ressel establish an even more general result, for a commutative semigroup with involution, for the closure of the cone of sums of squares of symmetric elements in the weighted $ell_1$-seminorm topology associated to an absolute value. In the present paper we give a new proof of these results which is based on Jacobi’s representation theorem. At the same time, we use Jacobi’s representation theorem to extend these results from sums of squares to sums of 2d-powers, proving, in particular, that for any integer $d>0$, the closure of the cone of sums of 2d-powers in the ring of real polynomials in the topology induced by the $ell_1$-norm is equal the cone consisting of all polynomials which are non-negative on the hypercube $[-1,1]^n$.
Source arXiv, 1109.0048
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.






ScienXe.org
» my Online CV
» Free

home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2025 - Scimetrica