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Subdivision schemes for iterated function systems
Author(s):
Charles
A.
Micchelli;
Thomas
Sauer;
Yuesheng
Xu
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1861-1872.
MSC (2000):
Primary 54C40, 14E20;
Secondary 46E25, 20C20
Posted:
December 7, 2000
MathSciNet review:
1814120
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Abstract:
We identify iterated function systems  and regular Borel measures  such that the matrix subdivision process relative to a finite family  converges if and only if  satisfies certain spectral properties.
References:
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- 1.
- Z. Chen, C. A. Micchelli, and Yuesheng Xu.
A construction of interpolating wavelets on invariant sets.
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Using the matrix refinement equation for the construction of wavelets on invariant sets.
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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 1/2,
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:
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
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
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