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Subdivision schemes for iterated function systems

Authors:	Charles A Micchelli Thomas Sauer Yuesheng Xu

Institution:	Department of Mathematics & Statistics, State University of New York, The University at Albany, Albany, New York 12222 ; Mathematisches Institut, Universität Erlangen--Nürnberg, Bismarckstr. 1 1/2, D--91054 Erlangen, Germany ; 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

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.

Keywords:	Subdivision iterated function systems spectral radius

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