Ergodic theorems along sequences and Hardy fields.

@article{Boshernitzan1996ErgodicTA,
title={Ergodic theorems along sequences and Hardy fields.},
author={M. Boshernitzan and M{\'a}t{\'e} Wierdl},
journal={Proceedings of the National Academy of Sciences of the United States of America},
year={1996},
volume={93 16},
pages={8205-7}
}

Let a(x) be a real function with a regular growth as x --> infinity. [The precise technical assumption is that a(x) belongs to a Hardy field.] We establish sufficient growth conditions on a(x) so that the sequence ([a(n)])(infinity)(n=1) is a good averaging sequence in L2 for the pointwise ergodic theorem. A sequence (an) of positive integers is a good averaging sequence in L2 for the pointwise ergodic theorem if in any dynamical system (Omega, Sigma, m, T) for f [symbol, see text] in L2(Omega… CONTINUE READING