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
收藏
页码：255 / 274
页数：20
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