# generalized functions

Published articles for generalized functions.

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## Generalized Functions -- A Primer

DevFeed: [Generalized Functions -- A Primer](<https://devfeed.tech/articles/generalized-functions-a-primer-40275.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/06/06/generalized-functions/>)

Published: 2012-06-06T20:57:05Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [abstraction](<https://devfeed.tech/topics/abstraction.md>), [Programming](<https://devfeed.tech/topics/programming.md>)

Tags: [abstraction](<https://devfeed.tech/tags/abstraction.md>), [fourier-analysis](<https://devfeed.tech/tags/fourier-analysis.md>), [fourier-transform](<https://devfeed.tech/tags/fourier-transform.md>), [functional-analysis](<https://devfeed.tech/tags/functional-analysis.md>), [generalized-functions](<https://devfeed.tech/tags/generalized-functions.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [primer](<https://devfeed.tech/tags/primer.md>), [programming](<https://devfeed.tech/tags/programming.md>), [theory](<https://devfeed.tech/tags/theory.md>)

### AI overview

This primer develops a more rigorous mathematical framework for Fourier transforms. It motivates the search for a class of functions that remains well behaved under the Fourier transform and its inverse, while avoiding divergent integrals.

### Source excerpt

Last time we investigated the naive (which I'll henceforth call "classical") notion of the Fourier transform and its inverse. While the development wasn't quite rigorous, we nevertheless discovered elegant formulas and interesting properties that proved useful in at least solving differential equations. Of course, we wouldn't be following this trail of mathematics if it didn't result in some worthwhile applications to programming. While we'll get there eventually, this primer will take us deeper down the rabbit hole of abstraction.