You are currently browsing the tag archive for the ‘trilinear Hilbert transform’ tag.

This is a well-known problem in multilinear harmonic analysis; it is fascinating to me because it lies barely beyond the reach of the best technology we have for these problems (namely, multiscale time-frequency analysis), and because the most recent developments in quadratic Fourier analysis seem likely to shed some light on this problem.

Recall that the Hilbert transform is defined on test functions $f \in {\mathcal S}({\Bbb R})$ (up to irrelevant constants) as

$Hf(x) := p.v. \int_{\Bbb R} f(x+t) \frac{dt}{t},$

where the integral is evaluated in the principal value sense (removing the region $|t| < \epsilon$ to ensure integrability, and then taking the limit as $\epsilon \to 0$.)

### Recent Comments

 Ben Crowell on A mathematical formalisation o… Law of Large Numbers… on The strong law of large n… rbcoulter on Finite time blowup for an aver… Anonymous on A differentiation identity Single Pixel Camera… on Compressed sensing and single-… Ubik on A differentiation identity Cathy O’Neil o… on A differentiation identity Anonymous on 245A, Notes 6: Outer measures,… Anonymous on 245A, Notes 6: Outer measures,… Anonymous on Why global regularity for Navi… Anonymous on Why global regularity for Navi… Sridhar Ramesh on 254A, Supplement 4: Probabilis… Entropy optimality:… on Determinantal processes Joker大人 | 倒霉的红眼 on The blue-eyed islanders puzzle Sergey_Ershkov on Finite time blowup for an aver…