an:01453269
Zbl 0985.37004
Assani, I.
Multiple return times theorems for weakly mixing systems
EN
Ann. Inst. Henri Poincar??, Probab. Stat. 36, No. 2, 153-165 (2000).
00064343
2000
j
37A25 93E25
ergodic dynamical system; weakly mixing systems
The author proves the pointwise convergence of the expression
\[
{1\over N}\sum^N_{n=0} a_n g(R^n z)
\]
where \((Z,K,\nu,R)\) is an ergodic dynamical system on a probability measure space \((Z,K,\nu)\), the sequence of scalars \(a_n\) has the form
\[
a_n= a_n(x, y_1,y_2,\dots, y_J)= \Biggl(\prod^H_{i= 1} f_i(T^{b,n}x)\Biggr) \Biggl(\prod^J_{j=1} g_j(S^n_j y_j)\Biggr),
\]
\((b_1,b_2,\dots, b_H)\in Z^H\), \(J\) is a positive integer, the functions \(f_i\) and \(g_j\) are bounded and \((X,F,\mu, T)\) and \((Y,G_j, m_j, S_j)\) are weakly mixing systems.
Liviu Goras (Ia??i)