The Short-Time Fourier Transform of Distributions of Exponential Type and Tauberian Theorems for Shift-Asymptotics

Sanja Kostadinova, Stevan Pilipović, Katerina Saneva, Jasson Vindas

We study the short-time Fourier transform on the space $\mathcal K'_1(\mathbb R^n)$ of distributions of exponential type. We give characterizations of $\mathcal K'_1(\mathbb R^n)$ and some of its subspaces in terms of modulation spaces. We also obtain various Tauberian theorems for the short-time Fourier transform.