Uniform partitions of frames of exponentials into Riesz sequences

Abstract

The Feichtinger Conjecture, if true, would have as a corollary that for each set $E\subset \T$ and $\Lambda \subset \mathbb{Z}$, there is a partition ${\Lambda }_1,...,{\Lambda }_N$ of $\mathbb{Z}$ such that for each $1\le i\le N$, $\{\exp (2\pi ix\lambda ):\lambda \in {\Lambda }_i\}$ is a Riesz sequence. In this paper, sufficient conditions on sets $E\subset \T$ and $\Lambda \subset \mathbb{R}$ are given so that $\{\exp (2\pi ix\lambda )1_E:\lambda \in \Lambda \}$ can be uniformly partitioned into Riesz sequences.

References in corpus (1)

• The Kadison-Singer Problem in Mathematics and Engineering