Stability of wavelet frames and Riesz bases, with respect to dilations and translations

CSpace

	Stability of wavelet frames and Riesz bases, with respect to dilations and translations
	Zhang, J
	2001
发表期刊	PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN	0002-9939
卷号	129 期号:4 页码:1113-1121
摘要	We consider the perturbation problem of wavelet frame (Riesz basis) {psi (j,k,a0,b0)} = {a(0)(nj/2) psi (a(0)(j)x - kb(0))} about dilation and translation parameters a(0) and b(0). For wavelet functions whose Fourier transforms have small supports, we give a method to determine whether the perturbation system {psi (j,k,a,b0)} is a frame (Riesz basis) and prove the stability about dilation parameter a(0) on Paley-Wiener space. For a great deal of wavelet functions, we give a definite answer to the stability about translation b(0). Moreover,if the Fourier transform <()over cap> has small support, we can estimate the frame bounds about the perturbation of translation parameter b(0). Our methods can be used to handle nonhomogeneous frames (Riesz basis).
关键词	frames stability wavelets
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000166283500022
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/16506
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, J
作者单位	Acad Sinica, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhang, J. Stability of wavelet frames and Riesz bases, with respect to dilations and translations[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,2001,129(4):1113-1121.
APA	Zhang, J.(2001).Stability of wavelet frames and Riesz bases, with respect to dilations and translations.PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,129(4),1113-1121.
MLA	Zhang, J."Stability of wavelet frames and Riesz bases, with respect to dilations and translations".PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 129.4(2001):1113-1121.