Shift-invariant subspaces and wavelets on local fields

被引：5
|
作者：
Behera, B. [1 ]
机构：
[1] Indian Stat Inst, Stat & Math Unit, Kolkata 700108, India
来源：
ACTA MATHEMATICA HUNGARICA | 2016年 / 148卷 / 01期
关键词：
wavelet; local field; frame; shift-invariant;
D O I：
10.1007/s10474-015-0558-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that every closed shift-invariant subspace of L (2)(K) is generated by the I >-translates of a countable number of functions, where K is a local field of positive characteristic and I > is an appropriate translation set. We use this result to provide a characterization of wavelets on such a field.
引用
收藏
页码：157 / 173
页数：17
相关论文
共 50 条
  • [1] Shift-invariant subspaces and wavelets on local fields
    B. Behera
    Acta Mathematica Hungarica, 2016, 148 : 157 - 173
  • [2] Dilates of shift-invariant spaces on local fields
    Behera, Biswaranjan
    PUBLICATIONES MATHEMATICAE DEBRECEN, 2023, 102 (3-4): : 261 - 284
  • [3] Sampling for shift-invariant and wavelet subspaces
    Hogan, JA
    Lakey, J
    WAVELET APPLICATIONS IN SIGNAL AND IMAGE PROCESSING VIII PTS 1 AND 2, 2000, 4119 : 36 - 47
  • [4] Harmonic maps and shift-invariant subspaces
    Aleman, Alexandru
    Pacheco, Rui
    Wood, John C.
    MONATSHEFTE FUR MATHEMATIK, 2021, 194 (04): : 625 - 656
  • [5] Harmonic maps and shift-invariant subspaces
    Alexandru Aleman
    Rui Pacheco
    John C. Wood
    Monatshefte für Mathematik, 2021, 194 : 625 - 656
  • [6] Closure of dilates of shift-invariant subspaces
    Soto-Bajo, Moises
    CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2013, 11 (10): : 1785 - 1799
  • [7] Local Sampling and Reconstruction in Shift-Invariant Spaces and Their Applications in Spline Subspaces
    Xian, Jun
    Sun, Wenchang
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2010, 31 (03) : 366 - 386
  • [8] Frames Associated with Shift-invariant Spaces on Local Fields
    Shah, Firdous A.
    Ahmad, Owais
    Rahimi, Asghar
    FILOMAT, 2018, 32 (09) : 3097 - 3110
  • [9] Generalized shift-invariant systems and frames for subspaces
    Christensen, O
    Eldar, YC
    JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2005, 11 (03) : 299 - 313
  • [10] THE STRUCTURE OF SHIFT-INVARIANT SUBSPACES OF SOBOLEV SPACES
    Aksentijevi'c, A.
    Aleksi'c, S.
    Pilipovi'c, S.
    THEORETICAL AND MATHEMATICAL PHYSICS, 2024, 218 (02) : 177 - 191
12345