Properties of Wiener-Wintner dynamical systems
Bulletin de la Société Mathématique de France, Volume 129 (2001) no. 3, p. 361-377

In this paper we prove the following results. First, we show the existence of Wiener-Wintner dynamical system with continuous singular spectrum in the orthocomplement of their respective Kronecker factors. The second result states that if fL p , p large enough, is a Wiener-Wintner function then, for all γ(1+1 2p-β 2,1], there exists a set X f of full measure for which the series n=1 f(T n x)e 2πinϵ n γ converges uniformly with respect to ϵ.

Dans cette note nous démontrons les résultats suivants. Tout d’abord nous montrons l’existence de systèmes dynamiques ergodiques du type Wiener Wintner ayant un spectre singulier continu dans l’orthogonal de leur facteurs de Kronecker.Ensuite nous montrons que si fL p est une fonction du type Wiener-Wintner alors, pour γ(1+1 2p-β 2,1] on peut trouver un ensemble X f de mesure pleine pour lequel la série n=1 f(T n x)e 2πinϵ n γ converge uniformément en ϵ.

DOI : https://doi.org/10.24033/bsmf.2402
Classification:  28D05,  11K38
Keywords: Wiener Wintner dynamical systems, Wiener Wintner functions, Kronecker factor
@article{BSMF_2001__129_3_361_0,
     author = {Assani, I. and Nicolaou, K.},
     title = {Properties of Wiener-Wintner dynamical systems},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {129},
     number = {3},
     year = {2001},
     pages = {361-377},
     doi = {10.24033/bsmf.2402},
     zbl = {0994.37004},
     mrnumber = {1881201},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2001__129_3_361_0}
}
Assani, I.; Nicolaou, K. Properties of Wiener-Wintner dynamical systems. Bulletin de la Société Mathématique de France, Volume 129 (2001) no. 3, pp. 361-377. doi : 10.24033/bsmf.2402. http://www.numdam.org/item/BSMF_2001__129_3_361_0/

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