Timeline for Half Laplacian; (definitions of) and regularity
Current License: CC BY-SA 3.0
3 events
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| Sep 10, 2014 at 18:04 | comment | added | Craig | @Christian. Ya, that is one way to define the half Laplacian. But there is also the other method where you add an extra dimension and consider a local problem. | |
| Sep 10, 2014 at 18:01 | comment | added | Christian Remling | I think you would normally define $(-\Delta)^{1/2}$ via the spectral theorem, with $-\Delta$ being the Dirichlet Laplacian. Then $T=(-\Delta)^{1/2}$ has the same eigenvectors $\phi_n$ as $-\Delta$, and $T^{-1}\phi_1=\lambda_1^{-1/2}\phi_1$. If you can't reproduce this result from a calculation with the integral kernel of $T^{-1}$, then this just means that you miscalculated somewhere. | |
| Sep 10, 2014 at 16:52 | history | asked | Craig | CC BY-SA 3.0 |