Timeline for Wiener Tauberian Theorem for nonunimodular group
Current License: CC BY-SA 3.0
12 events
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| Jan 5, 2012 at 18:03 | comment | added | Yemon Choi | Thank you for clarifying. It seems that Yulia Kuznetsova has answered your original question. If you want to find out about the Fourier algebra formulation of Wiener's theorem, I recommend the book of Reiter and Stegemann, which is itself based on some older notes/book of Reiter. | |
| Jan 5, 2012 at 11:44 | vote | accept | spr | ||
| Jan 5, 2012 at 11:42 | vote | accept | spr | ||
| Jan 5, 2012 at 11:44 | |||||
| Jan 5, 2012 at 10:27 | answer | added | Yulia Kuznetsova | timeline score: 7 | |
| Jan 5, 2012 at 9:41 | comment | added | spr | The ax+b group is non-unimodular. But perhaps WTT is true here. Is there other examples? | |
| Jan 5, 2012 at 9:11 | vote | accept | spr | ||
| Jan 5, 2012 at 11:42 | |||||
| Jan 5, 2012 at 6:30 | comment | added | spr | By WTT I meant the classical version. When the group $G$ is nonabelian, we state WTT as: if for $f\in L^1(G)$, the Fourier transform of $f$ is nonvanishing on every point of the unitary dual then the (both-sided) ideal generated by $f$ is dense in $L^1(G)$. Both-sided ideal can be changed to linear span of both-sided translations also. Even if the group is non-unimodular, $L^1(G)$ is a Banach algebra and invariant under left and right translations, though norm of $f$ and that of its right translation change. Am I right? I am not aware of other version of WTT. What is a good source? | |
| Jan 5, 2012 at 1:55 | history | edited | Yemon Choi |
added some tags
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| Jan 4, 2012 at 23:43 | answer | added | Alain Valette | timeline score: 6 | |
| Jan 4, 2012 at 15:10 | comment | added | Yemon Choi | Note also that all discrete groups are unimodular, even the Type II ones with nasty unitary duals; so the classical version of WTT in terms of the Fourier transform of functions on the group will be problematic. | |
| Jan 4, 2012 at 15:04 | comment | added | Yemon Choi | To provide extra context, could you please state the version of Wiener's Tauberian theorem that you mean in a non-abelian context? (The classical notion for $L^1$ group algebras is very reliant on the group being abelian; perhaps you have in mind one of the versions in terms of the Fourier algebra?) | |
| Jan 4, 2012 at 12:59 | history | asked | spr | CC BY-SA 3.0 |