Almost Everywhere Convergence of Riesz-Raikov Series

Volume 68 / 1995

Ai Fan Colloquium Mathematicum 68 (1995), 241-248 DOI: 10.4064/cm-68-2-241-248

Abstract

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 $∑_{n=1}^{∞} |c_n|^2 log^{2}n < ∞$.

Authors

  • Ai Fan

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