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The Feichtinger conjecture for exponentials asserts that the followingproperty holds for every fat Cantor subset B of the circle group: the set ofrestrictions to B of exponential functions can be covered by Riesz sets. Intheir seminal paper on the Kadison-Singer problem, Bourgain and Tzafriri provedthat this property holds if the characteristic function of B has Sobolevregularity. Their probability based proof does not explicitly construct a Rieszcover. They also showed how to construct fat Cantor sets whose characteristicfunctions have Sobolev regularity. However, these fat Cantor sets are notconvenient for numerical calculations. This paper addresses these concerns. Itconstructs a family of fat Cantor sets, parameterized by their Haar measure,whose characteristic functions have Sobolev regularity and their Fouriertransforms are Riesz products. It uses these products to perform computationalexperiments that suggest that if the measure of one of these fat Cantor sets Bis sufficiently close to one, then it may be possible to explicitly construct aRiesz cover for B using the Thue-Morse minimal sequence that arises in symbolictopological dynamics.

The Feichtinger Conjecture for Exponentials