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An Approach at the Binomial Transformation Problem Andrew Yingst
 

Summary: An Approach at the Binomial Transformation Problem
Andrew Yingst
University of South Carolina Lancaster
andy.yingst@gmail.com
The binomial transformation (also known as the Pascal adic transformation)
is a map defined on all but countably many points of {0, 1}N
by T : 0i
1j
10x
1j
0i
01x. This interesting map has a few interesting properties, including that
the two-sided orbit of a sequence (xn) is precisely the set of all images of (xn)
under a finite permutation. It is known that the ergodic measures for T are
precisely the Bernoulli trial measures, but it is unknown and has been of some
interest in recent years whether T is weak-mixing for any of these measures.
This question is the subject of the current talk.
Knowledge of an eigenfunction of T is essentially equivalent to knowledge
of how that eigenfunction integrates over subsets of {0, 1}N
. Using this Radon-

  

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

 

Collections: Mathematics