Timeline for Why is there no symplectic version of spectral geometry?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 19, 2019 at 10:45 | comment | added | Ben McKay | Thanks, now I see. | |
| Aug 19, 2019 at 10:43 | comment | added | Victor Ivrii | I forgot to credit 2) -- A.Shnirelman (then many papers about quantum chaos) | |
| Aug 19, 2019 at 9:21 | comment | added | Victor Ivrii | Ben McKay I completely agree that spectral could be applied to everything related to the spectrum of operator. The term spectral geometry reflects the amazing fact that spectral properties of operator are related to geometry (or dynamics). In 70-ies it was proven that 1) there is the second term in Weyl's asymptotics provided the set of periodic trajectories has measure 0 (J.J.Duistermaat & V. Guillemin) 2) there is an equidistribution of eigenfunctions provided the corresponding flow is ergodic Nothing like this for "symplectic Laplacian" | |
| Aug 19, 2019 at 8:49 | comment | added | Ben McKay | The term "spectrum" has a long history in physics related to the wave behaviour of light, the spectrum of colours of light, but has no historical relation to the notion of geodesic, until the twentieth century with theorems of various mathematicians. So I think that we could stretch the term "spectrum" to cover the eigenvalues of any operator which is somehow like that of the wave or Laplace operators, without invoking the notion of length. | |
| Aug 18, 2019 at 19:07 | history | answered | Victor Ivrii | CC BY-SA 4.0 |