Affine frames, GMRA's, and the canonical dual

被引：16

作者：

Bownik, M ^{[1
]}

Weber, E

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Wyoming, Dept Math, Laramie, WY 82071 USA

来源：

STUDIA MATHEMATICA | 2003年 / 159卷 / 03期

关键词：

D O I：

10.4064/sm159-3-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that if the canonical dual of an affine frame has the affine structure, with the same number of generators, then the core subspace V-0 is shift invariant. We demonstrate, however, that the converse is not true. We apply our results in the setting of oversampling affine frames, as well as in computing the period of a Riesz wavelet, answering in the affirmative a conjecture of Daubechies and Han. Additionally, we completely characterize when the canonical dual of a quasi-affine frame has the quasi-affine structure.

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页码：453 / 479

页数：27

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