English

A remark on dilation-and-modulation frames for $L^2(\mathbb{R}_+)$

Functional Analysis 2025-06-24 v1

Abstract

We show that every rationally sampled dilation-and-modulation system is unitarily equivalent with a multi-window Gabor system. As a consequence, frame theoretical results from Gabor analysis can be directly transferred to dilation-and-modulation systems.

Keywords

Cite

@article{arxiv.1912.01416,
  title  = {A remark on dilation-and-modulation frames for $L^2(\mathbb{R}_+)$},
  author = {Jakob Lemvig},
  journal= {arXiv preprint arXiv:1912.01416},
  year   = {2025}
}
R2 v1 2026-06-23T12:34:24.284Z