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Refinable functions on the Heisenberg group

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  • 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.

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


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