Do you know some investigation about high order discrete fourier transform?

For example, is it possible to extend FFT to high order ?

Thanks!

Zhiqiang

]]>Dear Tao,

Do you know some investigation about high order discrete fourier transform?

Thanks!

First line of preface: “…has been focused the analysis of…”

*[This will be corrected in the revised version, thanks. – T.]*

p.219. In the reference,I think that [Roth1964] should be [Roth1953]

*[This will be corrected in the revised version, thanks. – T.]*

Dear Gabor,

Ah, thanks for pointing this out. The book was based on a course I gave last spring (Mar-Jun 2010), back when only three of the six papers in Balazs’s series had appeared on the arXiv, and the connection to the combinatorial side of the subject (and in particular, to the inverse conjecture for the Gowers norms) was less clear. Of course I will update the references in view of the progress made in Balazs’s program (although the methods are closer to the ergodic theory side of the subject than the combinatorial one, which is the main focus of this particular text).

]]>I’m surprised not to see any mention of Balázs Szegedy’s work in the book. I’m not following the area very closely, but I have heard lectures by Balázs, and it seems to me important and relevant. Am I wrong? Or is there some other reason for the omission?

Thanks.

]]>Below are some simple corrections to be made.

p. 106 “thaat”.

P. 123″nilmaniofold”

p. 141. “Sectino 1.3”

p. 149. “to favorr”

p. 153. “See for instance [?] for more discussion. ” Of course, a Ctrl-F

search for “?” will take care of all these missing references.

p.219. Reference [Sh2009], article’s title is not in italics.

*[Corrected for the next revision, thanks – T.]*