Newtonian kernel

Summary

The Newtonian kernel on $\R^n$, for $n \ge 3$, is the function $k(x, y) = \abs{x - y}^{2-n}$ of two points. In space it is $1/\abs{x - y}$, the potential at $x$ of a unit mass at $y$ in Newton's law of gravitation. It is a constant multiple of the fundamental solution of the Laplacian translated to the pole $y$. Integrating it against a measure gives the Newtonian potential, the central object of classical potential theory in higher dimensions.