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Analysis of μ R,D -Orthogonality in Affine Iterated Function Systems

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Abstract

Let μ R,D be a self-affine measure associated with an expanding integer matrix R∈M n (ℤ) and a finite subset D⊆ℤn. In the present paper we study the μ R,D -orthogonality and compatible pair conditions. We also show that any set of μ R,D -orthogonal exponentials contains at most 3 elements on the generalized plane Sierpinski gasket and the number 3 is the best.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, People’s Republic of China

    Yan-Bo Yuan

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  1. Yan-Bo Yuan
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Correspondence to Yan-Bo Yuan.

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Yuan, YB. Analysis of μ R,D -Orthogonality in Affine Iterated Function Systems. Acta Appl Math 104, 151–159 (2008). https://doi.org/10.1007/s10440-008-9247-x

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  • DOI: https://doi.org/10.1007/s10440-008-9247-x

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