Uniform partitions of frames of exponentials into Riesz sequences

Abstract

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