CONSTRUCTION OF A RIESZ WAVELET BASIS ON LOCALLY COMPACT ABELIAN GROUPS

被引：1

作者：

Satyapriya ^{[1
]}

Kumar, Raj ^{[2
]}

机构：

[1] Univ Delhi, Dept Math, Delhi, India

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

来源：

JORDAN JOURNAL OF MATHEMATICS AND STATISTICS | 2022年 / 15卷 / 02期

关键词：

LCA Groups; Riesz Basis; Multiresolution Analysis; order of dilation; refinement equation; MULTIRESOLUTION ANALYSIS; BASES; FRAMES;

D O I：

10.47013/15.2.7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We have explored the concept of Riesz multiresolution analysis on a locally compact Abelian group G, and have extensively studied the methods of construction of a Riesz wavelet from the given Riesz MRA. We have proved that, if delta(alpha) is the order of dilation, then precisely delta(alpha)-1 functions are required to construct a Riesz wavelet basis for L-2(G). An example, supporting our theory and illustrating the methods developed, has also been discussed in detail.

引用

页码：255 / 274

页数：20

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