Norm Convergence in Ergodic Theory and the Behavior of Fourier Transforms
Joseph Max Rosenblatt · Canadian Journal of Mathematics · 1994
Abstract The Lp-norm convergence of weighted averages μnf is ergodic theory is equivalent to the pointwise convergence of the Fourier transforms . If h(γ) = , then the behavior of h determines when the Lp-norm limit of μnf is ∫f dm. The nature of such limit functions h is the focus of this article.