Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix

被引:88
作者
Han, B [1 ]
机构
[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada
关键词
tight wavelet frames; orthonormal wavelet bases; dilation matrix; smoothness; vanishing moments; Bessel wavelet sequences;
D O I
10.1016/S0377-0427(02)00891-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Tight wavelet frames and orthonormal wavelet bases with a general dilation matrix have applications in many areas. In this paper, for any d x d dilation matrix M, we demonstrate in a constructive way that we can construct compactly supported tight M-wavelet frames and orthonormal M-wavelet bases in L-2(R-d) of exponential decay, which are derived from compactly supported M-refinable functions, such that they can have both arbitrarily high smoothness and any preassigned order of vanishing moments. This paper improves several results in Battle (Comm. Math. Phys. 110 (1987) 601), Bownik (J. Fourier Anal. Appl. 7(2001) 489), Grochenig and Ron (Proc. Amer. Math. Soc. 126 (1998) 1101), Lemarie (J. Math. Pures Appl. 67 (1988) 227), and Strichartz (Constr. Approx. 9 (1993) 327). (C) 2003 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:43 / 67
页数:25
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