Refinable functions on the Heisenberg group

Heping Liu; Yu Liu

doi:10.3934/cpaa.2007.6.775

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2007, Volume 6, Issue 3: 775-787. Doi: 10.3934/cpaa.2007.6.775

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Refinable functions on the Heisenberg group

Heping Liu^1, and
Yu Liu^2,

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

Received: October 2005

Revised: August 2006

Published: August 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 42C40, 43A15, 26B35; Secondary: 65D15.

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