Abstract:We give a rigorous derivation of the Fourier transform of the Heaviside function within a framework for tempered distributions that is suitable for undergraduate engineering and mathematics students. The proofs rely on fundamental concepts typically taught in a freshman-level calculus course, including limits, generalized integrals, integration by parts and the Taylor Remainder Theorem.
| Comments: | 7 pages |
| Subjects: | Functional Analysis (math.FA) |
| MSC classes: | Primary 46-01, Secondary 46F10, 46F12 |
| Cite as: | arXiv:2605.22193 [math.FA] |
| (or arXiv:2605.22193v2 [math.FA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.22193 arXiv-issued DOI via DataCite |
From: Robert Dalang [view email]
[v1]
Thu, 21 May 2026 08:59:14 UTC (7 KB)
[v2]
Fri, 22 May 2026 15:30:22 UTC (7 KB)
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