Timeline for Can I relate the L1 norm of a function to its Fourier expansion?
Current License: CC BY-SA 2.5
7 events
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| Feb 10, 2016 at 19:03 | comment | added | Vanessa | I think it should be "integral of the absolute value of the Fourier transform" rather than "sum of the absolute values of the Fourier coefficients." The Fourier transform of a function on $\mathbb{Z}$ is a function on the circle $\mathbb{R}/\mathbb{Z}$. | |
| Apr 24, 2010 at 4:51 | comment | added | Gregory Putzel | That last comment is about the statistical problem, by the way. | |
| Apr 24, 2010 at 4:35 | comment | added | Gregory Putzel | I walked down the hall to where the high-energy physicists are and my friend pointed out that this is probably equivalent to the path-integral formulation of a single quantum mechanical particle in a V-shaped potential - which can be solved analytically in terms of Airy functions. I think he is exactly right and the averages can be worked out that way. So the specific question about L_1 norms is probably misguided (but prompted an interesting connection above), while the statistical problem which seemed more difficult to me might be surprisingly tractable analytically... | |
| Apr 24, 2010 at 4:04 | comment | added | fedja | Well, the question was actually whether one can write any decent expression that gives an essentially equivalent measure on the set of states (whatever that means), so we do not need an equality that is always true, just an approximation that is accurate enough most of the time. Unfortunately, as far as I can tell, this is also rather hard if not impossible... On the other hand, some averages like the one mentioned in the post may still be possible to compute. Let me think a bit... | |
| Apr 23, 2010 at 21:27 | vote | accept | Gregory Putzel | ||
| Apr 23, 2010 at 17:22 | comment | added | Andrey Rekalo | Could you possibly recommend any good book/survey article on the subject? | |
| Apr 23, 2010 at 16:32 | history | answered | gowers | CC BY-SA 2.5 |