A simple derivation of the Fourier transform of the Heaviside function
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917524503789568 |
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| author | Dalang, Robert C. |
| author_facet | Dalang, Robert C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22193 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A simple derivation of the Fourier transform of the Heaviside function Dalang, Robert C. Functional Analysis Primary 46-01, Secondary 46F10, 46F12 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. |
| title | A simple derivation of the Fourier transform of the Heaviside function |
| topic | Functional Analysis Primary 46-01, Secondary 46F10, 46F12 |
| url | https://arxiv.org/abs/2605.22193 |