Step Refinable Functions and Orthogonal MRA on Vilenkin Groups

被引：30

作者：

Lukomskii, Sergey F.

机构：

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2014年 / 20卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

Zero-dimensional groups; MRA; Vilenkin groups; Refinable functions; Wavelet bases; MULTIRESOLUTION ANALYSIS; WAVELET ANALYSIS; LOCAL-FIELDS;

D O I：

10.1007/s00041-013-9301-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We find necessary and sufficient conditions on refinable step function under which this function generates an orthogonal MRA in the -spaces on Vilenkin group . We consider a class of refinable step functions for which the mask m (0)(chi) is constant on cosets and its modulus |m (0)(chi)| has two values only: 0 and 1. We prove that any refinable step function phi from this class that generates an orthogonal MRA on Vilenkin group has Fourier transform with condition . We show the sharpness of this result, too.

引用

页码：42 / 65

页数：24

共 30 条

[1]

Agaev G.N., 1981, Multiplicative Systems of Functions and Harmonic Analysis on Zero-Dimensional Groups

[2] The Cauchy problems for evolutionary pseudo-differential equations over p-adic field and the wavelet theory [J].