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Results tagged with harmonic-analysis
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user 163699
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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Multipole expansion
In Simon's book Harmonic Analysis, example 3.5.12 shows:
Fix $x \in \mathbb{R}^{\nu}$ (with $\left.\nu \geq 3\right), x \neq 0$ and define $f$ on $\{y:| y|<| x |\}$ by
$$
f(y)=|x-y|^{-(\nu-2)}.
$$
The …
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