Abstract:It is shown that a certain class of Riesz product type measures on R is realized a spectral type of rank one flows. As a consequence, we will establish that some class of rank one flows has a singular spectrum. Some of the results presented here are even new for the Z-action. Our method is based, on one hand, on the extension of Bourgain-Klemes-Reinhold-Peyrière method, and on the other hand, on the extension of the Central Limit Theorem approach to the real line which gives a new extension of Salem-Zygmund Ce… Show more
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