Timeline for Uncertainty principle (really for Mellin, but never mind that!)
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 12, 2012 at 9:52 | comment | added | H A Helfgott | I should really add "shifts not allowed", since they give no gain in the original problem, but perhaps that calls for a change in the setup to reflect that. | |
| Nov 10, 2012 at 20:03 | comment | added | Ralph Furman | $e^{-e^{C x}}$ ends up hurting one of the bounds, but I think with $e^{-A e^x}$ you help the first super-exponentially without hurting the second at all, and when you add in the $e^{-x^2}$ you end up beating the second bound by something like $e^{-(\log t)^2}$ | |
| Nov 10, 2012 at 16:01 | comment | added | H A Helfgott | Thanks for this, but it's like the example I gave ($e^{e^{Cx}}$) - these variations due to rescaling improve one of the two aspects, but not the other (though one should be happy if they don't degrade it). I was wondering whether one can improve both... | |
| Nov 9, 2012 at 18:51 | history | edited | Ralph Furman | CC BY-SA 3.0 |
added 149 characters in body
|
| Nov 9, 2012 at 18:48 | comment | added | Ralph Furman | You can also replace the $1+x^2$ with any function growing in the strip, the best example being along the lines of $e^{A e^x}$. In fact, if you translate your original example you get something decaying much more quickly, without changing the modulus of the Fourier transform: $$e^{-A e^x}e^{B x}$$ | |
| Nov 9, 2012 at 11:12 | comment | added | H A Helfgott | This (roughly speaking) matches (a) and (b), perhaps a little more precisely than the example I gave. Do you think this is optimal? | |
| Nov 9, 2012 at 0:57 | history | answered | Ralph Furman | CC BY-SA 3.0 |