Spectrality of infinite Bernoulli convolutions

Let {b(k) - a(k)}(k=1)(infinity) be a sequence of positive integers with upper bound and let delta(E) be the uniformly discrete probability measure on the finite set E. For 0 < rho < 1, the infinite convolution mu(rho), {a(k), b(k)} = delta(rho{a1), (b1}) * delta(rho 2{a2, b2}) *...... is called an infinite Bernoulli convolution. In this paper, we investigate whenever there exists Lambda such that {e(-2 pi i lambda x)}(lambda is an element of Lambda) is an orthonormal basis for L-2(mu(p),({ak, bk})). (C) 2015 Elsevier Inc. All rights reserved.