# American Institute of Mathematical Sciences

September  2007, 6(3): 775-787. doi: 10.3934/cpaa.2007.6.775

## Refinable functions on the Heisenberg group

 1 LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, China 2 Department of Mathematics and Mechanics, University of Science and Technology, Beijing 100083, China

Received  October 2005 Revised  August 2006 Published  June 2007

The orthonormal wavelets associated with a multiresolution analysis are mainly determined by the corresponding refinable function. In this paper, we study the continuity of refinable functions on the Heisenberg group. The characterization of Lipschitz continuous refinable functions is given in terms of the uniform joint spectral radius. We also give an investigation of the refinable functions in the generalized Lipschitz spaces.
Citation: Heping Liu, Yu Liu. Refinable functions on the Heisenberg group. Communications on Pure & Applied Analysis, 2007, 6 (3) : 775-787. doi: 10.3934/cpaa.2007.6.775
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