Wavefront set of a smooth function

Asked Jan 28 '15 at 20:51

Active Jan 28 '15 at 20:51

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I'm trying to show that the wavefront set of a function $f \in C^{\infty}(\mathbb{R}^{n})$ is empty, $WF(f) = \emptyset$.

Can anyone help me prove this? This is my first exposition into wavefront sets so I have little progress with regards to workings out.

asked Jan 28 '15 at 20:51

Holtz

What is the definition of the wavefront set that you are using? Do you know that the Fourier transform of a Schwartz function is again a Schwartz function? – PhoemueX Jan 29 '15 at 09:30

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