Timeline for Functions orthogonal to harmonic functions
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 2, 2017 at 4:14 | comment | added | Willie Wong | @MathStudent: I think so. See the sketch of an argument I just included. (Instead of the surface measure, you can take a uniformly-dense thin shell in which case the computations can also be done exactly.) If I didn't make a stupid mistake in the computation, the argument should be stable under small perturbations and in particularly also allow you strictly positive (on some bounded domain $\Omega$) examples. | |
| Sep 2, 2017 at 4:10 | history | edited | Willie Wong | CC BY-SA 3.0 |
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| Sep 2, 2017 at 3:25 | comment | added | A random mathematician | @WillieWong You are right. But I forgot to mention that both $f_1$ and $f_2$ are positive functions. Do you think there would still be a counterexample? | |
| Sep 2, 2017 at 3:22 | vote | accept | A random mathematician | ||
| Sep 2, 2017 at 1:25 | comment | added | Fan Zheng | @WillieWong It doesn't matter, anyway. | |
| Sep 2, 2017 at 1:24 | comment | added | Fan Zheng | @MathStudent Note $\int f_1dx=\int f_2dx=0$, so $\int \lambda_1f_1dx=\int \lambda_2f_2dx=0$. | |
| Sep 2, 2017 at 1:21 | comment | added | A random mathematician | Thanks Willie. We need both integrals to be zero. Since $\int f_1dx=\int f_2dx$, doesn't the first condition force $\lambda_1=\lambda_2$? In your construction, both integrals don't vanish at the same time. | |
| Sep 2, 2017 at 0:46 | history | answered | Willie Wong | CC BY-SA 3.0 |