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arXiv · 2508.11639

On regularizations of the integral representation of Dirac delta function -- elementary approach

Grzegorz M. Koczan·Piotr Stachura
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Abstract

The article presents, in an elementary way, but with mathematical precision and without harm to the intuition, the path from the integral representation to the Dirac delta, starting with Schwartz's functional approach. Next, the considered representation is presented in a more intuitive sequential approach, formulated by Mikusi\'nski and Sikorski. Finally, we present the third regularization that can be related to Sato's approach to distributions.

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Grzegorz M. Koczan, Piotr Stachura. 2025-07-31. On regularizations of the integral representation of Dirac delta function -- elementary approach. https://arxiv.org/abs/2508.11639

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