The Existence of Infinite Orthogonal Sets of Moran Measures with Three-Element Digit Sets

Abstract

For n ≥ 1, let P_n > 1 and D_n ={ 0,a_n,b_n} ⊂ℤ, where a_n < b_n < p_n. In this paper we study the existence of infinite orthogonal exponential sets of moran measures which is generated by the sequence of integers {p_n}_n=1^∞ and the sequence of number sets {D_n}_n=1^∞. We obtain the necessary and sufficient conditions for infinite convolution μ to have infinite orthogonal exponential sets, this provides a good idea for constructing the spectrum of this function space.