Spectrality of Cantor–Moran measures with three-element digit sets

Abstract Let 0 < ρ < 1 {0<\rho<1} and let { a j , b j , n j } j = 1 ∞ {\{a_{j},b_{j},n_{j}\}_{j=1}^{\infty}} be a sequence of positive integers with an upper bound. Associated with them, there exists a unique Borel probability measure μ ρ , { 0 , a j , b j } , { n j } {\mu_{\rho,\{0,a_{j},b_{j}\},\{n_{j}\}}} generated by the following infinite convolution of discrete measures: μ ρ , { 0 , a j , b j } , { n j } = δ ρ n 1 ⁢ { 0 , a 1 , b 1 } ∗ δ ρ n 1 + n 2 ⁢ { 0 ,