Construction of Vector-valued Multivariate Wavelet Frame Packets

被引：0

作者：

Shah, Firdous Ahmad ^{[1
]}

Sheikh, Neyaz Ahmad ^{[2
]}

机构：

[1] Univ Kashmir, Dept Math, South Campus, Anantnag 192101, Jammu & Kashmir, India

[2] Natl Inst Technol, Dept Math, Srinagar 190006, Jammu & Kashmir, India

来源：

THAI JOURNAL OF MATHEMATICS | 2012年 / 10卷 / 02期

关键词：

Vector-valued wavelets; Wavelet packet; Wavelet frame packet; Dilation matrix; Splitting trick; Fourier transform;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the splitting trick coined by Chen [D.-R. Chen, On the splitting trick and wavelet frame packets, SIAM J. Math. Anal. 31 (4) (2000) 726-739] is used to construct vector-valued multivariate wavelet frame packets with an arbitrary dilation matrix A. It is shown that, as long as finitely many splitting steps are applied, the resulting sequence of functions is a frame of L-2(R-d)(r). If the matrix Q(xi) associated with the splitting is unitary, then the splitting can be applied infinitely many times to prove the existence of frame with the frame bounds as shown in Theorem 3.3.

引用

页码：401 / 414

页数：14

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