Comment on "Some novel delta-function identities"

TL;DR

This paper clarifies the conditions under which a proposed second derivative of 1/r is valid, providing a more general form applicable beyond smooth functions using dyadic notation.

Contribution

It introduces a generalized form of the second derivative of 1/r that does not require averaging over smooth functions, correcting previous assumptions.

Findings

The proposed form applies only when averaged over smooth functions.

A more general form is derived using dyadic notation.

The new form broadens the applicability of the derivative expression.

Abstract

We show that a form for the second partial derivative of $1/r$ proposed by Frahm and subsequently used by other workers applies only when averaged over smooth functions. We use dyadic notation to derive a more general form without that restriction.