Spectrality of a Class of Moran Measures on Rn.

Let { M k } k = 1 ∞ be a sequence of expansive matrices, and let { D k } k = 1 ∞ be a sequence of finite digit sets satisfying Z D k n = F q k n , where Z D k n = { x ∈ [ 0 , 1) n : ∑ d ∈ D k e 2 π i ⟨ d , x ⟩ = 0 } , F q k n = ( Z n q k ∩ [ 0 , 1) n) \ { 0 } and the sequence { q k } k = 1 ∞ is bounded with q k ≥ 2 . In this paper, we show that the associated integral Moran measure μ { M k } , { D k } is a spectral measure if and only if # D k = q k n for all k ≥ 1 and M k ∈ M n (q k Z) for all k ≥ 2 . [ABSTRACT FROM AUTHOR]