Decay of coefficients and approximation rates in Gabor Gaussian frames

2022/08/09 by Théophile Chaumont-Frelet, Chaumont-Frelet, T., Maxime Ingremeau +1
Computer Science · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA) #Optical and Acousto-Optic Technologies

paper · pdf · doi:10.48550/arxiv.2208.04853

openalex publication_date 2022/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this note is to present a self-contained proof of the fact that a function can be approximated using a linear combination of Gaussian coherent states, with a number of terms controlled in terms of the smoothness and of the decay at infinity of the function. This result can easily be obtained using advanced results on modulation spaces, but the proof presented here is completely elementary and self-contained.

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