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The short-time Fourier transform of distributions of exponential type and tauberian theorems for shift-asymptotics

Kostadinova Sanja (Ss. Cyril and Methodius University, Faculty of Electrical Engineering and Information Technologies, Skopje, Macedonia)
Pilipović Stevan (Department of Mathematics and Informatics, Novi Sad)
Saneva Katerina (Ss. Cyril and Methodius University, Faculty of Electrical Engineering and Information Technologies, Skopje, Macedonia)
Vindas Jasson (Ghent University, Department of Mathematics, Ghent, Belgium)

We study the short-time Fourier transform on the space K01(Rn) of distributions of exponential type. We give characterizations of K01(Rn) and some of its subspaces in terms of modulation spaces. We also obtain various Tauberian theorems for the short-time Fourier transform.

Keywords: Short-time Fourier transform, Tauberian theorems, modulation spaces, K01 and K1, distributions of exponential type, Silva tempered ultradistributions (tempered ultra-hyperfunctions), S-asymptotics, regularly varying functions