Timeline for Is there an upper bound on the number of critical points of a spherical harmonic on a local scale?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 23, 2018 at 13:43 | comment | added | fedja | You can cluster the critical points of the trigonometric polynomials at any speed you wish. cannot you? | |
| Jul 23, 2018 at 8:12 | comment | added | un umile appassionato | Pardon me if I have not understood correctly, but have you considered that the spherical disk shrinks as the degree of the spherical harmonic grows? The question is if you can cluster the critical points faster than the disk can shrink. | |
| Jul 20, 2018 at 12:49 | comment | added | fedja | If my memory does not betray me, you have the standard basis of the kind $e^{i m\varphi}P_m(\cos\theta)$ in the spherical coordinates where the polynomials $P_m$ are even and non-zero at $0$ for a certain parity of $m$. Thus, it suffices to construct a trigonometric polynomial on the circle (the equator) in frequencies of given parity that has a cluster of many critical points near, say, the "East pole", which is certainly possible. | |
| Jul 18, 2018 at 21:23 | review | First posts | |||
| Jul 18, 2018 at 23:04 | |||||
| Jul 18, 2018 at 21:19 | history | asked | un umile appassionato | CC BY-SA 4.0 |