Orthogonal bases of exponential functions for infinite convolutions

Jun Jie Miao, Hong Bo Zhao

Let $\mu$ denot the infinite convolution generated by $\{(N_k,B_k){\}}_{k=1}^{\infty }$ given by $$ μ=δ_{{N_1}^{-1}B_1}\astδ_{(N_1N_2)^{-1}B_2}\ast\dots\astδ_{(N_1N_2\cdots N_k)^{-1}B_k}…