Uniform partitions of frames of exponentials into Riesz sequences

TL;DR

This paper provides sufficient conditions under which sets of exponential functions, restricted to a subset of the torus, can be uniformly partitioned into Riesz sequences, advancing understanding related to the Feichtinger Conjecture.

Contribution

It introduces new sufficient conditions for partitioning exponential frames into Riesz sequences, specifically for functions supported on subsets of the torus.

Findings

Identifies conditions on sets E and Λ for uniform Riesz partitioning

Extends the theory of exponential frames and Riesz sequences

Provides a framework for approaching the Feichtinger Conjecture

Abstract

The Feichtinger Conjecture, if true, would have as a corollary that for each set $E\subset \T$ and $\Lambda \subset \Z$, there is a partition $\Lambda_1,...,\Lambda_N$ of $\Z$ such that for each $1\le i \le N$, $\{\exp(2\pi i x\lambda): \lambda \in \Lambda_i\}$ is a Riesz sequence. In this paper, sufficient conditions on sets $E\subset \T$ and $\Lambda\subset \R$ are given so that $\{\exp(2\pi i x\lambda) 1_E: \lambda \in \Lambda\}$ can be uniformly partitioned into Riesz sequences.