Calculus for the Delta Distribution

Abstract

A compendium of interesting identities involving the delta distribution in higher dimensional Euclidean space is presented, ready to use as a reference work whenever modelling with the delta function is involved. The formulæ are expressed as well in vector, as in Cartesian and spherical variables, the latter case being especially important since distributions in spherical coordinates have to be treated with the utmost care. Special attention is paid to an alter ego of the delta distribution, the so-called delta signumdistribution, acting on test functions showing a singularity at the origin, which appears, mostly unnoticed, when radial functions and negative powers of the radial distance are used.