| Popis: |
For a positive integer b ≥ 2 and two finite subsets D , C of Z with the same cardinality, we say that the pair ( b − 1 D , C ) is a compatible pair if the matrix [ e 2 π i d c / b ] d ∈ D , c ∈ C is orthogonal. Let { n j } j = 1 ∞ ⊆ N be any sequence of positive integers. In this paper we will show, under the condition of compatible pair ( b − 1 D , C ) , that the homogeneous Moran measure μ b , D , { n j } = δ b − n 1 D ⁎ δ b − ( n 1 + n 2 ) D ⁎ ⋯ ⁎ δ b − ( n 1 + n 2 + ⋯ n k ) D ⁎ ⋯ has an orthonormal basis consisting of exponentials. This extends a result of Łaba and Wang (2002) [22] and establishes the proof of Conjecture 1.1 of Fu and Wen (2015) [18] . |
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