A Cauchy-Dirac delta function

TL;DR

This paper explores the historical and mathematical foundations of the Dirac delta function, emphasizing its roots in 19th-century Fourier analysis and Cauchy's work on infinitesimals.

Contribution

It provides a historical perspective on the development of the delta function and clarifies Cauchy's infinitesimal approach to its definition.

Findings

Highlights the connection between Cauchy's infinitesimals and the delta function

Shows the delta function's roots in 19th-century analysis

Illuminates the historical development of the concept

Abstract

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.