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

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 ⊆ 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.