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Terence Tao has a book “Higher order Fourier analysis”, can anyone chip in on whether the two are related? Here is a video, it seems to focus on aaplications i
by gradschoolfail 3y ago
Terence Tao has a book “Higher order Fourier analysis”, can anyone chip in on whether the two are related?
Here is a video, it seems to focus on aaplications in number theory, but I cant tell as a layman
https://www.youtube.com/watch?v=nr2Xv9v9CZc https://www.youtube.com/watch?v=nr2Xv9v9CZc
For example, this is the tradFourier version of what hes trying to do
https://en.wikipedia.org/wiki/Hardy–Ramanujan–Littlewood_circle_method https://en.wikipedia.org/wiki/Hardy–Ramanujan–Littlewood_cir...
- shiandow 3y agoThe techniques in this article would be considered common knowledge for any of the prerequisite classes you'd need to take to be able to follow a course on Higher order Fourier analysis. I wouldn't say they're unrelated, but if you want to know whether both uses of the phrase "higher order" have any relation then no.
- gradschoolfail 3y agoThank you! I remember seeing in the Tao book a Fourier operator that looks something like the “integral” of exp(ik^2 x).. (or exp(ik x^2), haha) As a followup, is it possible to ELI5 roughly what Tao meant by “higher-order”?
- coherentpony 3y agoThe first paragraph of the preface on page 7 in the book gives an explicit example of “higher order”: https://terrytao.files.wordpress.com/2011/03/higher-book.pdf https://terrytao.files.wordpress.com/2011/03/higher-book.pdf
- gradschoolfail 3y agoLollol thats what i half remembered.. i guess then what Terence Tao meant by higher order is lower order in the featured artiicle!