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: 3643
Articles: 2'488'730
Articles rated: 2609

29 March 2024
 
  » arxiv » 0803.3767

 Article overview


Asymptotics of Toeplitz Matrices with Symbols in Some Generalized Krein Algebras
Alexei Yu. Karlovich ;
Date 26 Mar 2008
AbstractLet $alpha,etain(0,1)$ and [ K^{alpha,eta}:=left{ain L^infty(T): sum_{k=1}^infty |hat{a}(-k)|^2 k^{2alpha}<infty, sum_{k=1}^infty |hat{a}(k)|^2 k^{2eta}<infty ight}. ] Mark Krein proved in 1966 that $K^{1/2,1/2}$ forms a Banach algebra. He also observed that this algebra is important in the asymptotic theory of finite Toeplitz matrices. Ten years later, Harold Widom extended earlier results of Gabor SzegH{o} for scalar symbols and established the asymptotic trace formula [ operatorname{trace}f(T_n(a))=(n+1)G_f(a)+E_f(a)+o(1) quad ext{as} n oinfty ] for finite Toeplitz matrices $T_n(a)$ with matrix symbols $ain K^{1/2,1/2}_{N imes N}$. We show that if $alpha+etage 1$ and $ain K^{alpha,eta}_{N imes N}$, then the SzegH{o}-Widom asymptotic trace formula holds with $o(1)$ replaced by $o(n^{1-alpha-eta})$.
Source arXiv, 0803.3767
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.

browser claudebot






ScienXe.org
» my Online CV
» Free


News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2024 - Scimetrica