Characterisation of the Weyl-H\"ormander classes by time-frequency shifts
Abstract
We characterise the Weyl-H\"ormander symbol classes S(M,g) via the growth of the action of the corresponding on time-frequency shifts of a single test function. For this purpose, we introduce a geometric short-time Fourier transform which is well-suited for the analysis of S(M,g). We define new modulation spaces and achieve the characterisation of the Weyl-H\"ormander classes by showing that they are intersections of such modulation spaces suitable for the time-frequency characterisation.
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