A class of spectral Moran measures

Abstract Let { D k } k = 1 ∞ be a sequence of digit sets in N and let { b k } k = 1 ∞ be a sequence of integer numbers bigger than 1. We call the family { f k , D k ( x ) = b k − 1 ( x + d ) : d ∈ D k , k ⩾ 1 } a Moran iterated function system (IFS), which is a natural generalization of an IFS. We prove, under certain conditions in terms of ( b k , D k ) , that the associated Moran measure μ is a spectral measure, i.e., there exists a countable set Λ ⊂ N such that { e 2 π i λ x : λ ∈ Λ } is an orthonormal basis for L 2 ( μ ) .