Also see this metric space for signals : http://mathoverflow.net/q/193656/14414 : Mathematicians should take a serious note of it.

]]>It can revolutionize signal processing . I’ve got ample proofs for that, and would share if anyone interested to collaborate.

]]>

be the corresponding “maximal trilinear Hilbert transform”. Is there any conjecture about its boundedness?

*[I don’t know if it is explicitly stated in the literature, but based on analogy with the linear and bilinear Hilbert transform, the natural conjecture would be that it obeys the same estimates that the ordinary trilinear Hilbert transform does. -T.]*

Thanks for pointing out this subtle issue (and its fix)! This will be corrected in the next revision of the ms.

]]>thanks for the great read. There is a typo in the first display on p. 8 (v2), where all n’s should be replaced by -n’s. Also, at the end of p.15 (v2) follows from the counting lemma because the Lipschitz function in the integral is wlog bounded by 1.

Lastly, on p. 14 you pass to a product of nilmanifolds. It seems to me however that the product of the nilsequences g_i(n) need not be irrational, consider for instance the case when matching Taylor coefficients of two sequences are (almost) equal. The vector-valued version of the arithmetic regularity lemma that you mention of course removes this problem.

best,

pavel

Yes, one can work with for rationally commensurate coefficients and obtain similar results. However something strange happens in the non rationally commensurate case, one cannot easily discretise the problem and one now needs to develop a continuous version of the arithmetic regularity and counting lemmas (this should be possible but would require redoing a number of previous papers in the continuous setting). There is a previous paper of Christ in which a similar distinction between the commensurate and non-commensurate cases arose.

]]>