Last updated: August 15, 2018

Higher order Fourier analysis

Terence Tao

Graduate Studies in Mathematics, 142

American Mathematical Society, 2012

ISBN-10: 0-8218-8986-9

ISBN-13: 978-0-8218-8986-2

This continues my series of books derived from my blog. The preceding books in this series were “Structure and Randomness“, “Poincaré’s legacies“, “An epsilon of room“, “An introduction to measure theory“, and “Topics in random matrix theory“.

An online version of the text can be found here. It is based primarily on these lecture notes.

Errata:

- Page ???: In Exercise 1.1.17, should be .
- Page ???: In Exercise 1.1.20, should be .
- Page ???: Near the start of Section 1.3.2: the should be elements of rather than . “equilently” should be “equivalently”.
- Page 98: In the definition of a nilpotent filtered group , the additional hypothesis that is also nilpotent is required (this is automatic in the most important case , but not in general).
- Page 100: In the first paragraph, replace “starting from a point” with “starting with the base group , which is a point in the most important case “. Similarly, after Exercise 1.6.14, replace “starting from a point” by “starting from the base space , which is a point in the most important case “.
- Page 109: In Exercise 1.6.22, the argument indicated only works under the stronger hypothesis that are linearly independent modulo 1 over the integers. (To handle the general case, one either needs the more complicated quantitative (single-scale) relative van der Corput lemma in my paper with Green, or else rely on the ergodic theorem as was done in the paper of Leibman.)

Thanks to farlabb, Ben Green and Pavel Zorin for corrections.

### Like this:

Like Loading...

## 4 comments

Comments feed for this article

30 March, 2011 at 9:34 am

Higher order Fourier analysis « What’s new[…] finished writing the first draft of my thirdbook coming out of the 2010 blog posts, namely “Topics in random matrix theory“, which was based primarily on my graduate course in the topic, though it also contains […]

30 March, 2011 at 5:31 pm

eigenlambdaThanks! I’m a little past graduation, not yet in grad school, so I’ve been trying to figure stuff out on my own. Your previous measure theory book was incredibly helpful, and also all the lecture notes. And now something new! Christmas has come early this year indeed.

1 March, 2012 at 4:02 am

Non-Uniform Random Variate Generation and Fourier Analysis Textbooks | Multiply Leadership[…] the engineer looking for some technical background on Fourier analysis, see these free resources from Fields Medal winner Terry […]

29 September, 2015 at 11:08 am

PurpleHi Terence ! I am an undergraduate student studying physics. I have been figuring out stuff on my own .. But sometimes you get stuck :'( . I have been studying Fourier analysis.. Could you recommend me some really good material and how to go about understanding it .