Wiener-Wintner return-times ergodic theorem |
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Authors: | I Assani E Lesigne D Rudolph |
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Institution: | 1. Department of Mathematics, University of North Carolina at Chapel Hill, 27599, NC, USA 2. Département de Mathématique, Université Fran?ois Rabelais, Parc de Grandmont, 37200, Tours, France 3. Department of Mathematics, University of Maryland at College Park, 20740, MD, USA
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Abstract: | We state a new ergodic theorem, combining the Wiener-Wintner theorem and Bourgain’s theorem concerning the convergence of ergodic averages along return-times sequences. We consider ergodic averages of the form $$\frac{1}{N}\sum\limits_{n = 0}^{N - 1} {e^{in\theta } \cdot f'(S^n y) \cdot f(T^n x)} $$ and we show that the behaviour of these averages characterizes an algebraC of functions, which contains the Kronecker algebra and has interesting properties, linked with multiple recurrence ergodic theorems. |
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