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Results tagged with harmonic-analysis
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user 143419
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.
5
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2
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763
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How to calculate an integral over the complex unit sphere
We want to calculate the following integral over the complex unit sphere $S^{2n-1}$:
$$\int_{S^{2n-1}} \frac{1 }{|1 - \langle z, \zeta \rangle|^2} \, d\sigma(\zeta),$$
where $ z $ is a fixed point in …
- 113
1
vote
0
answers
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measure of Haar
Let $(G,K)$ be a Gelfand pair.
Why, for a function $f$ $K$-binvariant with respect to a compact subgroup $K$ of a group $G$, do we have the following equality:
$$ f(xy) = \int_K f(xky) \, dk$$
A funct …
- 113