Timeline for Density of irreducible matrix coefficients of a locally compact group
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 27, 2023 at 17:26 | comment | added | Pople | @LSpice It felt like since $f$ applies to functions, but I wrote the integral pointwise, there might be a problem (if I approximate the at each $g$, can I apply $f$ then ?). But on the other hand, $f$ should be the integral against a finite complex Radon measure on $K$ so with this point of view it should just amount to Fubini | |
| Apr 27, 2023 at 17:23 | comment | added | Pople | @BenjaminSteinberg Yes, I want infinite dimensional representation | |
| Apr 27, 2023 at 2:09 | comment | added | Yemon Choi | @BenjaminSteinberg In this context (abstract harmonic analysis) one usually allows unitary reps to be infinite-dimensional unless specified. Indeed, for the reasons you mention, the Gelfand-Raikov theorem would be false if one only allowed finite-dimensional unitary irreps | |
| Apr 26, 2023 at 20:54 | comment | added | Benjamin Steinberg | Do you allow infinite dimensional unitary reps? If you only allow finite dimensional you run into groups with no nontrivial finite dimensional reps | |
| Apr 26, 2023 at 19:40 | comment | added | LSpice | Integrals and continuous linear forms can be switched because integration is weighted addition followed by a limiting process. (But I haven't checked the rest of your argument.) | |
| S Apr 26, 2023 at 17:37 | review | First questions | |||
| Apr 26, 2023 at 18:05 | |||||
| S Apr 26, 2023 at 17:37 | history | asked | Pople | CC BY-SA 4.0 |