Multiresolution analysis, self-similar tilings and Haar wavelets on the Heisenberg group

Heping Liu; Yu Liu; Haihui Wang

doi:10.1016/S0252-9602(09)60102-8

Multiresolution analysis, self-similar tilings and Haar wavelets on the Heisenberg group

Heping Liu
, Yu Liu^*
, Haihui Wang

^*Corresponding author for this work

School of Mathematical Sciences

Peking University
University of Science and Technology Beijing

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L²(ℍ^d) by using self-similar tilings for the acceptable dilations on the Heisenberg group.

Original language	English
Pages (from-to)	1251-1266
Number of pages	16
Journal	Acta Mathematica Scientia
Volume	29
Issue number	5
DOIs	https://doi.org/10.1016/S0252-9602(09)60102-8
State	Published - Sep 2009

Keywords

42C15
42C40
43A15
52C99
Heisenberg group
multiresolution analysis
self-similar tilings
wavelets

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10.1016/S0252-9602(09)60102-8

Cite this

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title = "Multiresolution analysis, self-similar tilings and Haar wavelets on the Heisenberg group",

abstract = "In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L2(ℍd) by using self-similar tilings for the acceptable dilations on the Heisenberg group.",

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AU - Liu, Heping

AU - Liu, Yu

AU - Wang, Haihui

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N2 - In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L2(ℍd) by using self-similar tilings for the acceptable dilations on the Heisenberg group.

AB - In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L2(ℍd) by using self-similar tilings for the acceptable dilations on the Heisenberg group.

KW - 42C15

KW - 42C40

KW - 43A15

KW - 52C99

KW - Heisenberg group

KW - multiresolution analysis

KW - self-similar tilings

KW - wavelets

UR - https://www.scopus.com/pages/publications/65449129390

U2 - 10.1016/S0252-9602(09)60102-8

DO - 10.1016/S0252-9602(09)60102-8

M3 - 文章

AN - SCOPUS:65449129390

SN - 0252-9602

VL - 29

SP - 1251

EP - 1266

JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

IS - 5

ER -

Multiresolution analysis, self-similar tilings and Haar wavelets on the Heisenberg group

Abstract

Keywords

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