Demystifying 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 $\{T^k\ddot{I}†{\}}_{k=0}^{\infty }$ is a Carleson frame, then every subsequence of the form $\{T^{Nk+j_k}\ddot{I}†{\}}_{k=0}^{\infty }$ where $N\in \mathbb{N}$ and $0\le j_k<N$ is also a frame.