Timeline for A moment problem on $[0,1]$ in which infinitely many moments are equal
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| Aug 27, 2013 at 0:11 | vote | accept | Santhosh Kumar | ||
| Aug 26, 2013 at 20:08 | comment | added | Yemon Choi | @GeorgeLowther Of course. Thanks. (That will teach me to write before the first coffee of the day.) | |
| Aug 26, 2013 at 16:54 | comment | added | George Lowther | @yemon: the signed measure also vanishes on the constant functions. So, take its positive and negative components and scale them to get probability measures. | |
| Aug 26, 2013 at 16:19 | comment | added | Yemon Choi | @GeorgeLowther I agree that from Muntz-Szasz, a routine Hahn-Banach argument produces a signed measure not identically zero whose "moments vanish on S", but how do you then get two prob measures whose moments agree on $S$? (It's the norm 1 normalization condition which is bugging me, but I'm probably overlooking something stupid) | |
| Aug 26, 2013 at 9:07 | comment | added | Davide Giraudo | @GeorgeLowther Thank you! Now an interesting problem would be to exhibit, if it exists, an example where $\nu_k=\mu_k$ on a set $S$ for which $\sum_{n\in S}\frac 1n<\infty$, but the measures are not the same. | |
| Aug 26, 2013 at 9:05 | answer | added | Davide Giraudo | timeline score: 15 | |
| Aug 26, 2013 at 8:45 | comment | added | George Lowther | @Davide Giraudo: Interesting. Applying the Hahn-Banach theorem, that answers the question. $\mu=\nu$ is guaranteed if and only if $\sum_{n\in S}\frac1n=\infty$. | |
| Aug 26, 2013 at 7:51 | answer | added | Dima Pasechnik | timeline score: 3 | |
| Aug 26, 2013 at 2:02 | comment | added | Yemon Choi | @DouglasZare Agreed - the M-S theorem is hardly "obvious", not is it as far as I know part of the standard diet. | |
| Aug 26, 2013 at 2:00 | comment | added | Douglas Zare | Why does this question have two votes to close as "off-topic?" | |
| Aug 26, 2013 at 1:52 | comment | added | Yemon Choi | Trivial correction: it's the Müntz–Szász theorem en.wikipedia.org/wiki/M%C3%BCntz%E2%80%93Sz%C3%A1sz_theorem | |
| Aug 26, 2013 at 1:49 | history | edited | Santhosh Kumar | CC BY-SA 3.0 |
added 12 characters in body
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| Aug 25, 2013 at 21:58 | comment | added | Santhosh Kumar | @Davide Giraudo: Thanks for the Muntz-Szacz theorem! | |
| Aug 25, 2013 at 12:41 | review | Close votes | |||
| Aug 25, 2013 at 16:52 | |||||
| Aug 25, 2013 at 12:19 | history | edited | Michael Hardy | CC BY-SA 3.0 |
edited title
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| Aug 25, 2013 at 9:00 | review | First posts | |||
| Aug 25, 2013 at 9:47 | |||||
| Aug 25, 2013 at 8:41 | history | asked | Santhosh Kumar | CC BY-SA 3.0 |