Riesz potential

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] Reference

Solomentsev, E.D., "Riesz potential" SpringerLink Encyclopaedia of Mathematics (2001)

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