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arXiv · 1509.02005

Gabor frames and asymptotic behavior of Schwartz distributions

Sanja Kostadinova·Katerina Saneva·Jasson Vindas
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Abstract

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.

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Sanja Kostadinova, Katerina Saneva, Jasson Vindas. 2016-06-12. Gabor frames and asymptotic behavior of Schwartz distributions. https://doi.org/10.2298/aadm160511011k

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