"Anisotropic global wave front set for Gelfand-Shilov ultradistributions"Wahlberg, PatrikWe define and study a global wave front set for Gelfand-Shilov ultradistributions of Beurling type, with one positive parameter for decay and one for regularity. The wave front set is defined in terms of the lack of super-exponential decay of the short-time Fourier transform along curves of parabolic type. This gives a generalization of the global wave front set for the equal index case, defined by behaviour in cones in phase space. In dimension one the wave front set captures the behavior of certain chirp signals, namely oscillations of even power. We show microlocality of pseudo-differential operators with symbols in a space that gives continuous operators on Gelfand-Shilov spaces. |
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