Ergodic Theorems for Homogeneous Dilations
(English)Article in journal (Refereed) Submitted
In this paper we prove a general ergodic theorem for ergodic and measure preserving actions of R^d on standard Borel spaces. In particular, we cover R.L. Jones ergodic theorem on spheres. Our main theorem is concerned with ergodic averages with respect to homogeneous dilations of Rajchman measures on Rd . We establish mean convergence in Hilbert spaces for general Rajchman measures, and give a criterion in terms of the Fourier dimension of the measure when almost everywhere pointwise convergence holds. Applications include averages over smooth submanifolds and polynomial curves.
Dynamical Systems (math.DS); Classical Analysis and ODEs (math.CA)
IdentifiersURN: urn:nbn:se:kth:diva-13946OAI: oai:DiVA.org:kth-13946DiVA: diva2:328526
QC 201007052010-07-052010-07-052010-07-20Bibliographically approved