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Results tagged with harmonic-analysis
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user 32591
Harmonic analysis is a generalisation of Fourier analysis that studies the properties of functions. Check out this tag for abstract harmonic analysis (on abelian locally compact groups), or Euclidean harmonic analysis (eg, Littlewood-Paley theory, singular integrals). It also covers harmonic analysis on tube domains, as well as the study of eigenvalues and eigenvectors of the Laplacian on domains, manifolds and graphs.
10
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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 …
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6
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1
answer
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Stationary phase in spherical integral
I'm trying to find asymptotics for an oscillatory integral on $\mathbb{S}^{n-1}$, for which my advisor said I should use stationary phase arguments. The particular, he claims that:
If $\lambda\gg …
- 377
5
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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
2
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0
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Looking for some "nontrivial" examples of pseudodifferential operators/symbols
I'm reading up on $\Psi DO$'s and trying to find some examples of symbols that are not quite so trivial.
Obviously, the first example of a symbol that most people talk about is just a polynomial in $ …
- 377
2
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0
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Need to show bounded behavior of a particular Fourier transform
First let me be briefly state the relevant information to my problem:
$\beta(s) \in C_0^{\infty}([-1,1])$, and $\beta \equiv 1$ around $s=0$. The $\beta$ I'm using is an even function, but it doesn' …
- 377