A remark on dilation-and-modulation frames for L²(ℝ₊)

2019/12/03 by Lemvig, Jakob
#42C15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1912.01416

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.

Related

• Multi-window dilation-and-modulation frames on the half real line
• The density theorem of a class of dilation-and-modulation systems on the half real line
• Gabor frames for rational functions
• Decay of coefficients and approximation rates in Gabor Gaussian frames
• Gabor frame characterisations of generalised modulation spaces