Timeline for What dimension bound is known on the singular set of a linear combination of eigenfunctions of Laplacian?
Current License: CC BY-SA 3.0
4 events
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| Jul 14, 2015 at 22:58 | comment | added | Spencer | I am not bothered about making any stipulations about multiplicity or normalization. I guess I could really ask it for a general linear combination $f = a_1\phi_1 + \dots + a_m\phi_m$; $a_j \in \mathbb{R}$. | |
| Jul 14, 2015 at 22:54 | history | edited | Spencer | CC BY-SA 3.0 |
added some relevant context
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| Jul 14, 2015 at 11:15 | comment | added | Joonas Ilmavirta | The last dimension estimate does not hold on the torus $\mathbb R^n/\mathbb Z^n$. The function $f(x)=1-\cos(2\pi x_1)$ is the sum of the first two eigenfunctions (assuming this numbering and normalization is permitted) and the set $\mathcal S$ has dimension $n-1$. Do you want to normalize your eigenfunctions? If it's important that they are the first ones, how do you treat eigenvalues with multiplicity? | |
| Jul 14, 2015 at 10:04 | history | asked | Spencer | CC BY-SA 3.0 |