1. Spectrality of certain Moran measures with three-element digit sets
- Author
-
Zhi-Yong Wang, Xin-Han Dong, and Zong-Sheng Liu
- Subjects
Weak convergence ,Applied Mathematics ,010102 general mathematics ,Discrete set ,01 natural sciences ,Exponential function ,Convolution ,Combinatorics ,Product (mathematics) ,0103 physical sciences ,Orthonormal basis ,010307 mathematical physics ,0101 mathematics ,Element (category theory) ,Borel probability measure ,Analysis ,Mathematics - Abstract
Let D n = { 0 , a n , b n } = { 0 , 1 , 2 } ( m o d 3 ) , p n ∈ 3 Z + , n ≥ 1 , satisfy sup n ≥ 1 max { | a n | , | b n | } p n ∞ . It is well-known that there exists a unique Borel probability measure μ { p n } , { D n } generated by the following infinite convolution product μ { p n } , { D n } = δ p 1 − 1 D 1 ⁎ δ ( p 1 p 2 ) − 1 D 2 ⁎ ⋯ in the weak convergence. In this paper, we give some conditions to ensure that there exists a discrete set Λ such that the exponential function system { e 2 π i λ x } λ ∈ Λ forms an orthonormal basis for L 2 ( μ { p n } , { D n } ) .
- Published
- 2018