Timeline for Arveson spectrum for a unitary representation of a group on a Hilbert space
Current License: CC BY-SA 3.0
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Apr 12, 2015 at 12:59 | comment | added | Noix07 | I checked that strange minus sign: in Bratteli, Robinson (same pages as indicated previously), they actually write $U=e^{-i t H}$, as in physics. So there is no minus sign in the Fourier transform. | |
| Apr 12, 2015 at 11:35 | comment | added | Noix07 | I see the following link: Let $f\in L^1(\mathbb R)$ and $x\in\mathcal H$ $$U_f(x)=\int_{\mathbb R}f(t)\ e^{it H}\cdot x\ dt=\int_{\mathbb R}\left(\int_{\mathbb{R}}f(t)\ e^{it p} dP(p)\right)\cdot x\ dt=\left(\int_{\mathbb R}\hat{f}(-p)\ dP(p)\right)\cdot x$$ If $x$ is an eigenvector of $H$ with eigenvalue $p$, then $U_f(x)=\hat{f}(-p)\ x.$ It is stunning that the relation group and generator $U= e^{itH}$ is the same as the character of the group $\mathbb R$. Maybe related to mathoverflow.net/questions/202653/…. | |
| Apr 11, 2015 at 21:04 | history | asked | Noix07 | CC BY-SA 3.0 |