# Jean-Luc Bouchot

 Oct 18 answered How to calculate the regularization parameter in linear regression Mar 9 awarded Commentator May 2 comment Does there exist a function $f:[0,1] \to[0,1]$ such its graph is dense in $[0,1]\times[0,1]$?Would Hilbert curves be something of interest? Mar 22 revised Convergence of $L^p$ normsedited tags Mar 22 comment Convergence of $L^p$ normsWell, even though some points can be considered as outliers, they may carry a bit of information anyway, or we cannot distinguish if they proper information carrier or information destroyer sometimes (see for instance the problems in OCT imaging). As a basic example, you can think of the Hausdorff distance in image alignment: vividsolutions.com/jcs/images/caseStudies/polygonMatching/… The two sets seem to be pretty well aligned, if we take out the peak, but taking this peak into consideration tells us also that the shapes are quite different. Mar 22 asked Convergence of $L^p$ norms Mar 20 awarded Teacher Mar 20 answered Get a set of closest numbers from array? Mar 8 comment Measures on function spacesThanks guys, at least I have something to start with. Do you know any other of defining usefull (indeed Michael, I'not going to go far with yours! :) ) measures on such spaces? I'll eventually let you know how it goes, IF it goes any further! Mar 8 awarded Supporter Mar 8 asked Measures on function spaces Mar 7 asked Markov-like inequality for functionals Feb 27 comment Hilbert transform of white noiseI do have a problem with the accepted answer. I don't claim it's not correct or whatever, but I don't get something, if anyone could give more details that would be great. Here is my point: $\xi: L^2 \mapsto L^2$ (with the correct sets)... well why not. I m actually quite fine with that. Now, I start getting confused with the notations. Feb 27 comment Hilbert transform of white noise> Other notation for $\xi(g)$ includes $\xi(g)=\langle \xi,g\rangle= \int_\mathbb{R}ΞΎ(t)g(t)dt.$ I really don't get that point. Given $g\in L^2$, the definition of $\xi$ (or at least how it was introduced), then $\xi(g)$ should be in $L^2$ too. I first thought this notation would be justified by using Riesz representation theorem but anyway, we need a linear functional, which we, at the moment, do not have. Am I missing something? Feb 27 comment Hilbert transform of white noiseNow assuming my notation problems are not actually troubling. I don't get (this might be due to a lack of knowledge!) the conditions for $\xi$ to be white noise. The first one sounds strange to me. How can it be zero mean? I would have expected something like $\mathbb{E}[\xi(g)] = \mathbb{E}[g], \forall g$ Feb 27 comment Hilbert transform of white noiseIs there any further references on that topic? I feel a bit lost with that. I have indeed a more practical background and am not familiar with those theoretical aspects. Assume I have a signal $s \in L^2$ and a noisy measurement of it $\widetilde{s} = s+n$ with $n$ being my white noise. What I normally assume, is that $\mathbb{E}[n] = 0$. In that case, how can I find the $\xi$ as introduced above and write my $\widetilde{s} = \xi(s) =? \langle\xi,s\rangle$ ? Feb 1 awarded Scholar Feb 1 accepted Bounded monotonic non converging sequences Feb 1 comment Bounded monotonic non converging sequencesGot my example I was looking for... My question was actually not well posed. But you helped me a lot! This is what I was looking for Thanks again for your help! Feb 1 comment Bounded monotonic non converging sequencesCould it be that I had seen this thing in an article about constructive mathematics. I guess constructionism would reject the least upper bound property and as a consequence in this case this "every bounded monotonic sequence is convergent" wouldn't hold true. Am I getting it right?