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

 

Subdivision schemes for iterated function systems


Authors: Charles A. Micchelli, Thomas Sauer and Yuesheng Xu
Journal: Proc. Amer. Math. Soc. 129 (2001), 1861-1872
MSC (2000): Primary 54C40, 14E20; Secondary 46E25, 20C20
Published electronically: December 7, 2000
MathSciNet review: 1814120
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Abstract | References | Similar Articles | Additional Information

Abstract: We identify iterated function systems $\Phi$ and regular Borel measures $\mu$ such that the matrix subdivision process relative to a finite family $\mathcal{A}$ converges if and only if $\mathcal{A}$ satisfies certain spectral properties.


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Additional Information

Charles A. Micchelli
Affiliation: Department of Mathematics & Statistics, State University of New York, The University at Albany, Albany, New York 12222
Email: cam@math.albany.edu,cam@watson.ibm.com

Thomas Sauer
Affiliation: Mathematisches Institut, Universität Erlangen–Nürnberg, Bismarckstr. 1 $\frac12$, D–91054 Erlangen, Germany
Email: sauer@mi.uni-erlangen.de

Yuesheng Xu
Affiliation: Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105 and Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Email: xu@hypatia.math.ndsu.nodak.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05966-9
PII: S 0002-9939(00)05966-9
Keywords: Subdivision, iterated function systems, spectral radius
Received by editor(s): September 27, 1999
Published electronically: December 7, 2000
Additional Notes: The first author was supported by National Science Foundation under grants DMS–9504780 and DMS–9973427, by the Alexander von Humboldt foundation and by the Wavelets Strategic Research Programme, National University of Singapore, under a grant from the National Science and Technology Board and the Ministry of Education, Singapore
The second author was supported by Deutsche Forschungsgemeinschaft with a Heisenberg fellowship, Sa 627/6
The third author was supported by National Science Foundation under grants DMS–9504780 and DMS–9973427, by the Alexander von Humboldt Foundation and by the “One Hundred Outstanding Young Chinese Scientists” program of the Chinese Academy of Sciences
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society