Everywhere divergence of the one-sided ergodic Hilbert transform for circle rotations by Liouville numbers
نویسندگان
چکیده
We prove some results on the behavior of infinite sums of the form ∑ f ◦ T(x) 1 n , where T : S → S is an irrational circle rotation and f is a mean-zero function on S. In particular, we show that for a certain class of functions f , there are Liouville α for which this sum diverges everywhere and Liouville α for which the sum converges everywhere.
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