Timeline for The identity element of a compact group is a limit point of any "polynomial sequence"
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Oct 24, 2012 at 6:43 | vote | accept | user25235 | ||
| Oct 24, 2012 at 6:43 | vote | accept | user25235 | ||
| Oct 24, 2012 at 6:43 | |||||
| Oct 23, 2012 at 20:12 | answer | added | Asaf | timeline score: 1 | |
| Oct 23, 2012 at 19:50 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Oct 23, 2012 at 19:47 | comment | added | GH from MO | @km: Thanks for the clarification. I just posted an argument that shows that the values $P(n)$ can be replaced by any van der Corput sequence of positive integers. | |
| Oct 23, 2012 at 19:45 | answer | added | GH from MO | timeline score: 7 | |
| Oct 23, 2012 at 16:09 | comment | added | user25235 | @GH: when $G$ is a torus, one can conclude by a standard Weyl's sums argument. But by "a straightforward generalisation" I meant "replace the torus by $G$ throughout the proof" (since noncommutativity causes no trouble in our ultralimits). @Terry Tao: Thanks for the elegant reduction. Your argument using Peter-Weyl theorem works also in the noncommutative case (which could arise if one considers instead sequences $n \mapsto g^{P(n)}h^{Q(n)}$ - where the ultralimit argument still applies), in which case we only have to consider (a finite list of) compact Lie groups. | |
| Oct 23, 2012 at 15:20 | comment | added | GH from MO | @Terry: Thank you. For tori I am not surprised there is an "elementary" proof. | |
| Oct 23, 2012 at 14:46 | comment | added | Terry Tao | By passing to the orbit closure of g, which is monothetic and hence abelian, one can assume G is compact abelian, hence the inverse limit of finite union of torii. From this it is not difficult to reduce to the torus case. | |
| Oct 23, 2012 at 14:40 | comment | added | GH from MO | @km: The mentioned Theorem 7.2 is a statement about a torus. I am interested in a reference for noncommutative compact groups as in your post. | |
| Oct 23, 2012 at 14:31 | answer | added | Ramiro de la Vega | timeline score: 6 | |
| Oct 23, 2012 at 13:10 | comment | added | user25235 | For example : this is a straightforward generalisation of theorem 7.2 in the following article of Vitaly Bergelson math.osu.edu/~bergelson.1/VBContempMathUltrafiltersEtc.pdf . | |
| Oct 23, 2012 at 12:32 | comment | added | GH from MO | Can you give a reference to any proof? | |
| Oct 23, 2012 at 12:10 | history | asked | user25235 | CC BY-SA 3.0 |