A+ CATEGORY SCIENTIFIC UNIT

Ergodic averages with generalized weights

Volume 173 / 2006

Doğan Çömez, Semyon N. Litvinov Studia Mathematica 173 (2006), 103-128 MSC: Primary 28D05; Secondary 37A99. DOI: 10.4064/sm173-2-1

Abstract

Two types of weighted ergodic averages are studied. It is shown that if $F=\{ F_n\} $ is an admissible superadditive process relative to a measure preserving transformation, then a Wiener–Wintner type result holds for $F$. Using this result new good classes of weights generated by such processes are obtained. We also introduce another class of weights via the group of unitary functions, and study the convergence of the corresponding weighted averages. The limits of such weighted averages are also identified.

Authors

  • Doğan ÇömezDepartment of Mathematics
    North Dakota State University
    Fargo, ND 58105-5075, U.S.A.
    e-mail
  • Semyon N. LitvinovDepartment of Mathematics
    Penn State University at Hazleton
    Hazleton, PA 18202, U.S.A.
    e-mail

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