Geodesic
Almost Everywhere Convergence of Riesz-Raikov Series
Colloquium Mathematicum, Tome 68 (1995) no. 2, pp. 241-248

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let T be a d×d matrix with integer entries and with eigenvalues >1 in modulus. Let f be a lipschitzian function of positive order. We prove that the series $∑_{n=1}^{∞} c_n f(T^{n}x)$ converges almost everywhere with respect to Lebesgue measure provided that $∑_{n=1}^{∞} |c_n|^2 log^{2}n ∞$.
DOI : 10.4064/cm-68-2-241-248
Keywords: Riesz-Raikov series, quasi-orthogonality, Bernoulli measures

Ai Fan 1

1 
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Ai Fan. Almost Everywhere Convergence of Riesz-Raikov Series. Colloquium Mathematicum, Tome 68 (1995) no. 2, pp. 241-248. doi: 10.4064/cm-68-2-241-248

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