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

2025/07/31 by Grzegorz Marcin Koczan, Grzegorz M. Koczan, Koczan, Grzegorz M. +2 · 1 voice
Mathematics · Physics and Astronomy · #46F99 #97199 #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #History and Overview (math.HO) #Mathematical Physics (math-ph) #advanced mathematical theories #math-ph #math.HO

paper · pdf · doi:10.48550/arxiv.2508.11639

openalex publication_date 2025/07/31 · arxiv published 2025/07/31 · arxiv updated 2025/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Mikusiński and Sikorski. Finally, we present the third regularization that can be related to Sato's approach to distributions.

Discussions

• Grzegorz M. Koczan, Piotr Stachura: On regularizations of the integral representation of Dirac delta function -- elementary approach https://arxiv.org/abs/2508.11639 https://arxiv.org/pdf/2508.11639 h [bsky, 0 points, 0 comments]

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