Convergence of cascade sequence on the Heisenberg group
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- by Heping Liu and Yu Liu PDF
- Proc. Amer. Math. Soc. 134 (2006), 1413-1423 Request permission
Abstract:
The investigation of convergence of cascade sequence plays an important role in wavelet analysis on the Euclidean space and also in wavelet analysis on the Heisenberg group. This paper characterizes the $L^p(\mathbf H^d)$ $(1\leq p\leq \infty )$-convergence of cascade sequence on the Heisenberg group in terms of the $p$-norm joint spectral radius of a collection of matrices associated with the refinement sequence and gives a sufficient condition.References
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Additional Information
- Heping Liu
- Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- MR Author ID: 262443
- Email: hpliu@math.pku.edu.cn
- Yu Liu
- Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- Email: liuyu@math.pku.edu.cn
- Received by editor(s): July 13, 2004
- Received by editor(s) in revised form: December 13, 2004
- Published electronically: October 7, 2005
- Additional Notes: This research was supported by the National Natural Science Foundation of China (No. 10371004) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20030001107)
- Communicated by: David R. Larson
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1413-1423
- MSC (2000): Primary 40A30, 42C15, 39B99, 65F15
- DOI: https://doi.org/10.1090/S0002-9939-05-08108-6
- MathSciNet review: 2199188