Haar system on a product of zero-dimensional compact groups

被引：4
作者：
Lukomskii, Sergei F. [1 ]
机构：
[1] Saratov NG Chernyshevskii State Univ, Dept Math & Mech, Saratov, Russia
来源：
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2011年 / 9卷 / 03期
基金：
俄罗斯基础研究基金会;
关键词：
Compact zero-dimensional groups; Characters; Haar functions; Wavelet bases; MULTIRESOLUTION ANALYSIS; ORTHOGONAL WAVELETS;
D O I：
10.2478/s11533-011-0012-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work, we study the problem of constructing Haar bases on a product of arbitrary compact zero-dimensional Abelian groups. A general scheme for the construction of Haar functions is given for arbitrary dimension. For dimension d=2, we describe all Haar functions.
引用
收藏
页码：627 / 639
页数：13
相关论文
共 24 条
  • [1] Agaev G.N., 1981, Multiplicative Systems of Functions and Harmonic Analysis on Zero-Dimensional Groups
  • [2] p-Adic Multiresolution Analysis and Wavelet Frames
    Albeverio, S.
    Evdokimov, S.
    Skopina, M.
    [J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2010, 16 (05) : 693 - 714
  • [3] ALBEVERIO S, 2009, T MAT I STEKLOVA, P265
  • [4] Albeverio S., 2010, London Mathematical Society Lecture Note Series, V370, DOI 10.1017/CBO9781139107167
  • [5] A wavelet theory for local fields and related groups
    Benedetto, JJ
    Benedetto, RL
    [J]. JOURNAL OF GEOMETRIC ANALYSIS, 2004, 14 (03) : 423 - 456
  • [6] BENEDETTO RL, 2004, CONT MATH, V345, P27
  • [7] Evdokimov SA, 2009, T I MAT MEKH URO RAN, V15, P135
  • [8] Orthogonal wavelets with compact support on locally compact abelian groups
    Farkov, YA
    [J]. IZVESTIYA MATHEMATICS, 2005, 69 (03) : 623 - 650
  • [9] Orthogonal wavelets on direct products of cyclic groups
    Farkov, Yu. A.
    [J]. MATHEMATICAL NOTES, 2007, 82 (5-6) : 843 - 859
  • [10] Golubov B. I., 1968, Sib. Mat. Zh., V9, P297
123