WAVELET FRAMES IN L2 (Rd)

被引：2

作者：

Poumai, Khole Timothy ^{[1
]}

Kaushik, Shiv Kumar ^{[2
]}

机构：

[1] Univ Delhi, Motilal Nehru Coll, Dept Math, Delhi, India

[2] Univ Delhi, Kirori Mal Coll, Dept Math, Delhi, India

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2020年 / 50卷 / 02期

关键词：

wavelet frames; Riesz wavelet bases; orthonormal wavelet basis; OPV frames;

D O I：

10.1216/rmj.2020.50.677

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain a necessary and sufficient condition for the existence of wavelet frames. We define and study the synthesis and analysis operators associated with wavelet frames. We discuss some applications of operator value (OPV) frames in the theory of wavelet frames. Also, we discuss the minimal property of wavelet frame coefficients and study the property of over completeness of wavelet frames. Various characterizations of wavelet frame, Riesz wavelet basis and orthonormal wavelet basis are given. Further, dual wavelet frames are discussed and a characterization of dual wavelet frames is given. Finally, we give a characterization of a pair of biorthogonal Riesz bases.

引用

页码：677 / 692

页数：16

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