Timeline for In what sense does the Laplacian on compact intervals converge to one on all of $\mathbb{R}$?
Current License: CC BY-SA 4.0
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| Jan 16 at 18:26 | comment | added | Christian Remling | @Isaac: $\Delta$ on $L^2(\mathbb R)$ has purely absolutely continuous spectrum, so strictly speaking there are no eigenfunctions to converge to, but if we instead look at spectral measures, which for $\Delta$ on $L^2(-n,n)$ will be point measures with weights determined by suitably chosen eigenfunctions, then we will have convergence on this level. | |
| Jan 16 at 16:15 | comment | added | Isaac | Thank you! I wonder how the eigenfunctions behave under the limit. Perhaps they converge under some metric topology to the eigenfunctions of $\Delta$ on whole $\mathbb{R}$? | |
| Jan 15 at 21:51 | vote | accept | Isaac | ||
| Jan 15 at 18:39 | history | answered | Christian Remling | CC BY-SA 4.0 |