A sharper stability bound of Fourier frames期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

A sharper stability bound of Fourier frames

Authors:	Weifeng Su Xingwei Zhou

Institution:	(1) Nankai Institute of Mathematics, Nankai University, 300071 Tianjin, P.R. China

Abstract:	Given a real sequence {_n}_n. Suppose that $\left\{ {e^{i\lambda _n x} } \right\}_{n \in \mathbb{Z}}$ is a frame for L²–, ] with bounds A, B. The problem is to find a positive constant L such that for any real sequence {_n}_n with ¦_n –_n¦ <L, $\left\{ {e^{i\mu _n x} } \right\}_{n \in \mathbb{Z}}$ is also a frame for L²–, ]. Balan 1] obtained $L_R = \tfrac{1}{4} - \tfrac{1}{\pi }$ arcsin $\left( {\tfrac{1}{{\sqrt 2 }}\left( {1 - \sqrt {\tfrac{A}{B}} } \right)} \right)$ . This value is a good stability bound of Fourier frames because it covers Kadec's 1/4-theorem $\left( {L_R = \tfrac{1}{4}ifA = B} \right)$ and is better than $L_{DS} = \tfrac{1}{\pi }\ln \left( {1 + \sqrt {\tfrac{A}{B}} } \right)$ (see Duffin and Schaefer 3]). In this paper, a sharper estimate is given.

Keywords:	42C15
本文献已被 SpringerLink 等数据库收录！