Georg Zimmermann, Universität Hohenheim (Koautor: Karlheinz Gröchenig)
We show how the Björck spaces of ultra-rapidly decaying test functions and the Gelfand-Shilov spaces of type can be described via the Short Time Fourier Transform. We also point out connections with the so-called modulation spaces (e.g., see ). These spaces are characterized by the global behaviour of the short-time Fourier transform of its members. They are the appropriate frame-work to describe function spaces by means of Gabor frames, in a way similar to the characterization of Besov spaces via wavelet expansions.
|||H.G. Feichtinger, K. Gröchenig, and D. Walnut, Wilson Bases and Modulation Spaces, Math. Nachr. 155 (1992), pp. 7-17.|