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- W2953249932 abstract "We define the Gabor wave front set $WF_G(u)$ of a tempered distribution $u$ in terms of rapid decay of its Gabor coefficients in a conic subset of the phase space. We show the inclusion $$WF_G(a^w(x,D) u) subseteq WF_G(u), u in mathscr S'(mathbb R^d), a in S_{0,0}^0,$$ where $S_{0,0}^0$ denotes the Hormander symbol class of order zero and parameter values zero. We compare our definition with other definitions in the literature, namely the classical and the global wave front sets of Hormander, and the $cS$-wave front set of Coriasco and Maniccia. In particular, we prove that the Gabor wave front set and the global wave front set of Hormander coincide." @default.
- W2953249932 created "2019-06-27" @default.
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- W2953249932 date "2012-07-24" @default.
- W2953249932 modified "2023-09-27" @default.
- W2953249932 title "The Gabor wave front set" @default.
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