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

DOI:
https://doi.org/10.1090/S0002-9939-05-08118-9

Published electronically:
July 18, 2005

MathSciNet review:
2180904

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-05-08118-9

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.