Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (5): 1251-1266.doi: 10.1016/S0252-9602(09)60102-8

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MULTIRESOLUTION ANALYSIS, SELF-SIMILAR TILINGS AND HAAR WAVELETS ON THE HEISENBERG GROUP

 LIU He-Ping, LIU Yu, WANG Hai-Hui   

  1. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, |China Department of Mathematics and Mechanics, School of Applied Science, University of Science and Technology Beijing, Beijing 100083, China Department of Applied Mathematics, Beihang University, Beijing 100083, China
  • Received:2007-08-16 Online:2009-09-20 Published:2009-09-20
  • Supported by:

    Sponsored by the NSFC (10871003, 10701008, 10726064),  and the Specialized Research Fund for the Doctoral Program of Higher Education of China (2007001040)

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 $L^2({\mathbb H}^d)$ by using self-similar tilings for the acceptable dilations on the Heisenberg group.

Key words: Heisenberg group, multiresolution analysis,  wavelets, self similar tilings

CLC Number: 

  • 43A15
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