Timeline for Invertibility of discrete Laplacian
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 5, 2020 at 3:46 | vote | accept | JustWannaKnow | ||
| May 30, 2020 at 1:11 | history | became hot network question | |||
| May 29, 2020 at 19:18 | comment | added | Nate Eldredge | It shouldn't be too surprising that the injectivity, and the spectral properties in general, are affected by the choice of boundary conditions. You see this in the continuous situation too: the Dirichlet Laplacian on a nice domain is injective, the Neumann Laplacian isn't. | |
| May 29, 2020 at 18:00 | answer | added | gmvh | timeline score: 5 | |
| May 29, 2020 at 17:53 | comment | added | Michael Engelhardt | Yes, this is well known. The derivative operator with periodic boundary conditions has a zero mode and is not invertible. This remains true for your discretized version. A wealth of information about much more than this is in any textbook on lattice gauge theory. | |
| May 29, 2020 at 17:11 | history | asked | JustWannaKnow | CC BY-SA 4.0 |