Uniform partitions of frames of exponentials into Riesz sequences

The Feichtinger conjecture, if true, would have as a corollary that for each set E ⊂ [0, 1] and Λ ⊂ Z, there is a partition Λ1, . . . , ΛN of Z such that for each 1 i N, {exp(2πixλ): λ ∈ Λi } is a Riesz sequence. In this paper, sufficient conditions on sets E ⊂ [0, 1] and Λ ⊂ R are given so that {exp(2πixλ)1E : λ ∈ Λ} can be uniformly partitioned into Riesz sequences