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Pointwise characteristic factors for the multiterm return times theorem
 

Summary: Pointwise characteristic factors for the
multiterm return times theorem
Idris Assani, Kimberly Presser
Department of Mathematics, UNC Chapel Hill, NC 27599,
(e-mail: assani@math.unc.edu)
Department of Mathematics, Shippensburg University, PA 27517
(e-mail: kjpres@ship.edu)
(Received December 30, 2010)
Abstract. This paper is an update and extension of a result the authors first proved
in 2003. The goal of this paper is to study factors which are known to be L2
-
characteristic for certain nonconventional averages and prove that these factors are
pointwise characteristic for the multiterm return times averages.
In memory of Dan Rudolph.
Pointwise Characteristic Factors 1
1. Introduction
A major result in ergodic theory in the late 1980's was the proof of the return
times theorem by J. Bourgain [8] (which was later simplified by J. Bourgain,
H. Furstenberg, Y. Katznelson, D. Ornstein in [9]). This theorem created a key
strengthening of the Birkhoff's Pointwise Ergodic Theorem [7].

  

Source: Assani, Idris - Department of Mathematics, University of North Carolina at Chapel Hill

 

Collections: Mathematics