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Results tagged with harmonic-analysis
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user 121820
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.
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votes
Why is $\frac{1}{|x|^{n-2}}u(\frac{x}{|x|^2})$ harmonic if $u$ is harmonic?
Here is another explanation which has various generalizations.
Denote by $L = \Delta + \frac{n-2}{4(n-1)}R$ the conformal Laplacian of a Riemannian manifold $(M^n,g)$ (my convention is that $\Delta$ i …
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