HOROWITZ SEMINAR

PROBABILITY, ERGODIC THEORY and DYNAMICAL SYSTEMS


Monday, 26/1/2009, at 14:30 in: room 210, Schreiber Bldg.

Christophe Cuny (Equipe ERIM, University of New-Caledonia)

will speak

On the a.s. convergence of the one-sided ergodic Hilbert transform.


Abstract:


We show that for T a Dunford-Schwartz operator on a probability space (X,Σ,μ) and f ε L1(X,μ),
whenever the one-sided ergodic Hilbert transform ∑n≥1Tnf ⁄ n converges in norm,
it converges μ-a.s.

In the case where T is the (unitary) operator induced by a measure-preserving (invertible) transformation,
this answers a question of Gaposhkin.

To suggest a talk (yours, or someone elses), contact Jon. Aaronson: aaro at post dot tau dot ac dot il

Back to: Jon Aaronson's homepage.

    Last update on 20/1/09.