, Volume 104, Issue 2, pp 151-159
Date: 29 May 2008

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 RM n (ℤ) and a finite subset D⊆ℤ n . 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.