In a previous work by Laba and Wang, it was proved that whenever there is a Hadamard triple (N, D, L), then the associated one-dimensional self-similar measure mu N,D generated by maps N-1(x + d) with d is an element of D, is a spectral measure. In this paper, we introduce pro duct-form digit sets for finitely many Hadamard triples (N, Ak, Lk) by putting each triple into different scales of N. Our main result is to prove that the associated self-similar measure mu N,D is a spectral measure. This result allows us to show that pro duct-form self-similar tiles are spectral sets as long as the til...
