We consider equally-weighted Cantor measures mu(q,b) arising from iterated function systems of the form b(-1)(x + i), i = 0, 1, ..., q - 1, where q < b. We classify the (q, b) so that they have infinitely many mutually orthogonal exponentials in L-2(mu(q,b)). In particular, if q divides b, the measures have a complete orthogonal exponential system and hence spectral measures. Improving the construction by Dutkay et al. (2009) [3], we characterize all the maximal orthogonal sets Lambda when q divides b via a maximal mapping on the q-adic tree in which all elements in Lambda are represented uniq...
