A RANGE FUNCTION APPROACH TO SHIFT-INVARIANT SPACES ON LOCALLY COMPACT ABELIAN GROUPS

被引：20

作者：

Gol, R. A. Kamyabi ^{[1
]}

Tousi, R. Raisi ^{[1
]}

机构：

[1] Ferdowsi Univ Mashhad, Dept Math, Mashhad 91775, Iran

来源：

INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING | 2010年 / 8卷 / 01期

关键词：

Second countable locally compact abelian group; shift-invariant space; range function; frame; Riesz family;

D O I：

10.1142/S0219691310003365

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

This paper develops several aspects of shift-invariant spaces on locally compact abelian groups. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift-invariant subspaces of L-2(G) in terms of range functions. Utilizing these functions, we generalize characterizations of frames and Riesz bases generated by shifts of a countable set of generators from L-2(R-n) to L-2(G).

引用

页码：49 / 59

页数：11

共 14 条

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