Dualities in Physics and Fourier Transforms

In many articles, authors compare physical dualities to Fourier transforms.

For example:

1. Joseph Polchinski, in his article "String Duality" (hep-th/9607050v2), writes: "Weak/strong duality […] is similar to a Fourier transform, where a function which becomes spread out in position space can become very narrow in momentum space. Here though, the Fourier transform is in a complicated nonlinear field space."

2. Cumrun Vafa, in his article "Geometric Physics"(hep-th/9810149v1), writes: "…duality […] in some sense is a nonlinear infinite-dimensional generalization of the Fourier transform."

I understand their points, but since these articles are from 1996 and 1998, I wanted to know if someone has, since then, found a more general/precise mathematical definition that would make dualities manifest (paraphrasing Nathan Seiberg – see link below).

Summing up, what I am looking for is:

1. Some procedure to identify if a theory has a dual theory.
2. A method to determine this dual theory.

Quoting Nathan Seiberg (www.icts.res.in/sites/default/files/KAWS2018-2018-01-08-Nathan-Seiberg-1.pdf), "we should not be surprised by duality!"

I don’t need (nor have any hope of finding) a rigorous mathematical definition. Just something slightly more general and expressed in more mathematical terms (compared to the papers I mentioned above) would already be fantastic.