  The Feichtinger conjecture for exponentials asserts that the following
property holds for every fat Cantor subset B of the circle group: the set of
restrictions to B of exponential functions can be covered by Riesz sets. In
their seminal paper on the Kadison-Singer problem, Bourgain and Tzafriri proved
that this property holds if the characteristic function of B has Sobolev
regularity. Their probability based proof does not explicitly construct a Riesz
cover. They also showed how to construct fat Cantor sets whose characteristic
functions have Sobolev regularity. However, these fat Cantor sets are not
convenient for numerical calculations. This paper addresses these concerns. It
constructs a family of fat Cantor sets, parameterized by their Haar measure,
whose characteristic functions have Sobolev regularity and their Fourier
transforms are Riesz products. It uses these products to perform computational
experiments that suggest that if the measure of one of these fat Cantor sets B
is sufficiently close to one, then it may be possible to explicitly construct a
Riesz cover for B using the Thue-Morse minimal sequence that arises in symbolic
topological dynamics.
