Almost Everywhere Convergence of Riesz-Raikov Series

• Autorzy: Ai Hua Fan
• Języki publikacji: EN

Abstrakty

EN

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 $∑_{n=1}^{∞} |c_n|^2 log^{2}n < ∞$.

Słowa kluczowe

EN

Riesz-Raikov series; quasi-orthogonality; Bernoulli measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1995
• Tom: 68
• Numer: 2
• Strony: 241-248

Daty

wydano

1995

otrzymano

1994-01-31

poprawiono

1994-07-08

Twórcy

autor

Ai Hua Fan

• Mathématiques (Bât. I), Université de Cergy-Pontoise, 8, le Campus, 95033 Cergy-Pontoise, France

Bibliografia

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• [7] J. Rosenblatt, Convergence of series of translations, Math. Ann. 230 (1977), 245-272.
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