Timeline for Spectral geometry: asymptotic sequences of subspaces of $L^2(M)$ and the geometry of $M$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 30, 2015 at 14:38 | vote | accept | B K | ||
| Sep 29, 2015 at 14:15 | answer | added | Liviu Nicolaescu | timeline score: 1 | |
| Sep 21, 2015 at 21:46 | comment | added | Paul Siegel | $L^2(M)$ is a separable Hilbert space for any closed connected Riemannian manifold $M$, and any two separable Hilbert spaces are isomorphic. So by itself $L^2(M)$ knows nothing about the geometry of $M$. The general philosophy of spectral theory is that a bare Hilbert space is boring, but a Hilbert space equipped with an operator (or better yet, an algebra of operators) is very interesting. In particular, I know of no source of examples of subspaces $V_j$ that are not eigenspaces of some operator (generally elliptic pseudodifferential). | |
| Sep 21, 2015 at 21:19 | history | asked | B K | CC BY-SA 3.0 |