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Results tagged with micro-local-analysis
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user 32591
10
votes
2
answers
6k
views
Fourier transform of compactly supported distribution is smooth
My advisor made the comment that if $u\in \mathcal{E}'$ is a compactly supported distribution, then $\hat{u}(\xi)\in C^{\infty}(\mathbb{R}^n)$ is actually a smooth function (not merely a distribution …
- 377
1
vote
0
answers
243
views
Interpretation of Smoothing Operators as $\Psi$DO's
In most of the computations I've seen involving pseudodifferential operators (referred to as $\Psi$DO's from now on) we do not have true equality. Instead we often only have equivalence of operators, …
- 377
5
votes
1
answer
226
views
Why do people study Weyl asymptotics and partial-spectral-projections?
The major focus of the research that my advisor has me doing centers around the idea of asymptotic behavior of partial-spectral-projections on compact manifolds. In a few sentences, here is the contex …
- 377