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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On multivariate subdivision schemes with nonnegative finite masks


Author: Xinlong Zhou
Journal: Proc. Amer. Math. Soc. 134 (2006), 859-869
MSC (2000): Primary 65D17, 26A15, 26A18
Published electronically: July 18, 2005
MathSciNet review: 2180904
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08118-9
PII: S 0002-9939(05)08118-9
Keywords: Nonnegative mask, subdivision scheme, zonotope.
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.