Gabor frames and asymptotic behavior of Schwartz distributions

We obtain characterizations of asymptotic properties of Schwartz distribution by using Gabor frames. Our characterizations are indeed Tauberian theorems for shift asymptotics (S-asymptotics) in terms of short-time Fourier transforms with respect to windows generating Gabor frames. For it, we show that the Gabor coefficient operator provides (topological) isomorphisms of the spaces of tempered distributions $\mathcal{S}'(\mathbb{R}^d)$ and distributions of exponential type $\mathcal{K}'_{1}(\mathbb{R}^{d})$ onto their images.

Jaar van publicatie:2016

BOF-keylabel:ja

IOF-keylabel:ja

BOF-publication weight:0.1

CSS-citation score:1

Auteurs:International

Authors from:Higher Education

Toegankelijkheid:Open