Riesz potential

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In mathematics, a Riesz potential is a scalar function $V_{\alpha} : \mathbb{R}^{n} \to \mathbb{R}$ , $n \geq 2$ , of the form

$V_{\alpha} (x)= \int_{{\mathbb{R}}^n} \frac{1}{| x - y |^{\alpha}} \, \mathrm{d} \mu (y),$

where $α > 0$ and $μ$ is a Borel measure whose support is a compact subset of $\mathbb{R}^{n}$ . When $n \geq 3$ and $α = n - 2$ , the Riesz potential coincides with the Newtonian potential.

The Riesz potential is named after the Hungarian mathematician Marcel Riesz.

[edit] References

Solomentsev, E.D. (2001), “Riesz potential”, in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104

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