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If $(x_0,\xi_0)\in\mathbb{R}^{2n}$ is a given point in phase space, how do I construct a compactly supported distribution $u$ which has

WF$(u)=\{(x_0,t\xi_0) | t>0\}$ ?

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How do you define wavefront? – Davide Giraudo Jul 16 '12 at 19:33
I would like to know the answer to this question also. I am using the definition that $(x_0 , \xi_0)$ is NOT in $WF(u)$ if and only if there is a pseudodifferential operator $P$ of order 0, elliptic at $(x_0 , \xi_0)$, such that $Pu \in \mathcal S$ (Schwarz space). – user15464 Oct 21 '12 at 0:58

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