Dilates of shift-invariant spaces on local fields

被引：0

作者：

Behera, Biswaranjan ^{[1
]}

机构：

[1] Indian Stat Inst, Stat & Math Unit, 203 BT Rd, Kolkata 700108, India

来源：

PUBLICATIONES MATHEMATICAE DEBRECEN | 2023年 / 102卷 / 3-4期

关键词：

shift-invariant spaces; local fields; frames; Bessel systems; Parseval wavelet; generalized MRA; space of negative dilates; MULTIRESOLUTION ANALYSIS; CONSTRUCTION; WAVELETS; SYSTEMS;

D O I：

10.5486/PMD.2023.9271

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be a local field of positive characteristic. We prove that if the space V of negative dilates of a Parseval wavelet of L2(K) has dimension function finite on a set of positive measure, then the intersection of the dilates of V is trivial. We also construct an example of a frame wavelet of L2(K) whose space of negative dilates is all of L2(K). The frame wavelet can be chosen to have frame bounds arbitrarily close to 1 and it has a dual frame wavelet.

引用

页码：261 / 284

页数：24