# functional analysis

Published articles for functional analysis.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## Carnival of Mathematics #197

DevFeed: [Carnival of Mathematics #197](<https://devfeed.tech/articles/carnival-of-mathematics-197-40448.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2021/09/01/carnival-of-mathematics-197/>)

Published: 2021-09-01T08:00:00Z

Content type: article

Language: en

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

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Graphics](<https://devfeed.tech/topics/graphics.md>), [Simulation](<https://devfeed.tech/topics/simulation.md>), [Data Science](<https://devfeed.tech/topics/data-science.md>)

Tags: [carnival](<https://devfeed.tech/tags/carnival.md>), [dataset](<https://devfeed.tech/tags/dataset.md>), [fibonacci](<https://devfeed.tech/tags/fibonacci.md>), [folding](<https://devfeed.tech/tags/folding.md>), [functional-analysis](<https://devfeed.tech/tags/functional-analysis.md>), [geometric-series](<https://devfeed.tech/tags/geometric-series.md>), [graphics](<https://devfeed.tech/tags/graphics.md>), [inner-product](<https://devfeed.tech/tags/inner-product.md>), [knot-theory](<https://devfeed.tech/tags/knot-theory.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [oeis](<https://devfeed.tech/tags/oeis.md>), [sequence](<https://devfeed.tech/tags/sequence.md>), [sieve](<https://devfeed.tech/tags/sieve.md>), [simulation](<https://devfeed.tech/tags/simulation.md>), [umap](<https://devfeed.tech/tags/umap.md>), [visualization](<https://devfeed.tech/tags/visualization.md>)

### AI overview

The 197th Carnival of Mathematics introduces the number 197 and highlights mathematical and technical topics including curve untangling, folding equilateral triangles without measurement, and criticism of UMAP and t-SNE dimensionality reduction.

### Source excerpt

Welcome to the 197th Carnival of Mathematics! 197 is an unseemly number, as you can tell by the Wikipedia page which currently says that it has "indiscriminate, excessive, or irrelevant examples." How deviant. It's also a Repfigit, which means if you start a fibonacci-type sequence with the digits 1, 9, 7, and then continue with $ a_n = a_{i-3} + a_{i-2} + a_{i-1}$, then 197 shows up in the sequence. Indeed: 1, 9, 7, 17, 33, 57, 107, 197, ...

## 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.