## On multivariate subdivision schemes with nonnegative finite masks

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## Abstract:

We study the convergence of multivariate subdivision schemes with nonnegative finite masks. Consequently, the convergence problem for the multivariate subdivision schemes with nonnegative finite masks supported on centered zonotopes is solved. Roughly speaking, the subdivision schemes defined by these masks are always convergent, which gives an answer to a question raised by Cavaretta, Dahmen and Micchelli in 1991.## References

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## Additional Information

**Xinlong Zhou**- Affiliation: Department of Mathematics, China Jiliang University, 310018 Hangzhou, People’s Republic of China – and – Department of Mathematics, University of Duisburg-Essen, D-47057 Duisburg, Germany
- Email: zhou@math.uni-duisburg.de
- Received by editor(s): March 22, 2004
- Received by editor(s) in revised form: October 8, 2004
- Published electronically: July 18, 2005
- 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), 859-869 - MSC (2000): Primary 65D17, 26A15, 26A18
- DOI: https://doi.org/10.1090/S0002-9939-05-08118-9
- MathSciNet review: 2180904