Demystifying Carleson Frames

TL;DR

This paper investigates the properties of Carleson frames, proving that certain subsequences of these frames also maintain their frame properties, thus advancing understanding of their structure and stability.

Contribution

It proves a conjecture that subsequences of Carleson frames, formed by specific index patterns, are also frames, revealing new stability properties of these systems.

Findings

Subsequences of Carleson frames of a specific form are also frames.

The paper confirms a recent conjecture about Carleson frame subsequences.

Enhances understanding of the structure and stability of Carleson frames.

Abstract

We study spanning properties of Carleson systems and prove a recent conjecture on frame subsequences of Carleson frames. In particular, we show that if $\{T^k\varphi\}_{k=0}^\infty$ is a Carleson frame, then every subsequence of the form $\{T^{Nk+j_k}\varphi\}_{k=0}^\infty$ where $N\in\mathbb{N}$ and $0 \leq j_k < N$ is also a frame.