Subdivision schemes for iterated function systems
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- by Charles A. Micchelli, Thomas Sauer and Yuesheng Xu PDF
- Proc. Amer. Math. Soc. 129 (2001), 1861-1872 Request permission
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.References
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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 $\frac 12$, 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
- MR Author ID: 214352
- Email: xu@hypatia.math.ndsu.nodak.edu
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1861-1872
- MSC (2000): Primary 54C40, 14E20; Secondary 46E25, 20C20
- DOI: https://doi.org/10.1090/S0002-9939-00-05966-9
- MathSciNet review: 1814120