Timeline for Decomposition of $L^2(\Gamma \backslash H)$ into irreducible representations using the spectral theorem
Current License: CC BY-SA 4.0
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Feb 11, 2019 at 19:28 | comment | added | Kimball | I haven't checked carefully, but I think this is essentially in Tamagawa's paper "On Selberg's trace formula" (see Theorem 2). | |
| Feb 10, 2019 at 4:10 | comment | added | Yemon Choi | OK, I must confess I've never checked how the proof of the result mentioned by Arthur goes (something like this is in an introductory book on harmonic analysis by Deitmar, IIRC?) but I think this is the same idea as in the usual proof of the Peter-Weyl theorem, see e.g. Prop. 7 in terrytao.wordpress.com/2011/01/23/… | |
| Feb 10, 2019 at 3:57 | comment | added | D_S | Yes, you can find an orthonormal basis of eigenvectors for real eigenvalues which tend to zero. | |
| Feb 10, 2019 at 3:22 | comment | added | Yemon Choi | Are you familiar with what the spectral theorem for compact self-adjoint operators says? | |
| Feb 9, 2019 at 20:26 | history | asked | D_S | CC BY-SA 4.0 |