EXPONENTIAL ORTHONORMAL BASES OF CANTOR–MORAN MEASURES.

Let μ { p n , d n } be a Cantor–Moran measure given by the infinite convolution of finite measures with equal probability μ { p n , d n } = δ p 1 − 1 { 0 , d 1 } ∗ δ (p 1 p 2) − 1 { 0 , d 2 } ∗ ⋯ , where { p n , d n } ⊂ ℤ and 0 < d n < p n for n ≥ 1. In this paper, we present a complete characterization for maximal orthogonal sets of exponentials of L 2 (μ { p n , d n }) in terms of maximal mappings. As its application, we give a sufficient condition for a maximal orthogonal set to be a basis. [ABSTRACT FROM AUTHOR]