Timeline for Is each multiplicative linear functional on $L^1(SL(2,R):SO(2,R))$ is triviall?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 31, 2015 at 13:07 | comment | added | Yemon Choi | For one-sided invariant functions, I guess the book of Reiterand Stegemann may have something; but it may not deal with the particular case that you are after | |
| Jan 31, 2015 at 11:45 | comment | added | B.Gillan | Dear Yemon Choi, Can you refer to a good reference in this regard. | |
| Jan 29, 2015 at 12:13 | comment | added | Yemon Choi | Oh, my mistake: I was thinking of SO(3)-bi-invariant functions. Your question is asking about one-sided SO(3)-invariant functions, right? | |
| Jan 29, 2015 at 4:51 | comment | added | B.Gillan | Thank you. But it isn't commutative B.al. | |
| Jan 28, 2015 at 14:44 | comment | added | Yemon Choi | If memory serves right, $L^1(SL(2,R),SO(2,R))$ is a commutative Banach algebra -- this is a Gelfand pair, isn't it? -- and it is moreover semisimple. I don't recall the proof but I think you can write down explicit characters on this algebra using the spherical functions associated to this Gelfand pair. | |
| Jan 28, 2015 at 5:42 | history | asked | B.Gillan | CC BY-SA 3.0 |