NON-SPECTRAL PROBLEM ON INFINITE BERNOULLI CONVOLUTION

摘要

Let {d(k)}(k=1)(infinity) be an upper-bounded sequence of positive integers and let dE be the uniformly discrete probability measure on the finite set E. For 0 < rho < 1, the infinite convolution mu(rho),{0, d(k)} := delta(rho{0,d1}) * delta(rho 2{0,d2}) * ... is called an infinite Bernoulli convolution. The non-spectral problem on mu(rho,{0,dk}) is to investigate the cardinality of orthogonal exponentials in L-2(mu(rho,{0,dk})). In this paper, we give a characterization of this problem by classifying the values of rho.

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