Timeline for Find an element with given periodicity
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 8, 2020 at 15:13 | history | bounty ended | Kung Yao | ||
| Dec 7, 2020 at 8:29 | comment | added | Bertram Arnold | Up to some constants, the map from $L^2(\mathbb R,\mathbb C)$ is exactly the isomorphism between representations of the canonical commutation relations I described abstractly in my answer. In particular, the eigenfunctions of the harmonic oscillator (i.e. the Hermite functions) get sent to the basis that I constructed. It seems like this gives an interesting Fourier-type series for the Weierstrass sigma function, which at least I didn't know before! | |
| Dec 7, 2020 at 5:20 | comment | added | Noam D. Elkies | Hm, come to think about it the orthogonal basis coming from Hermite functions probably ends up being equivalent to the one that Bertram Arnold constructed with connections and differential operators. The two approaches might be complementary $-$ the derivation of $e^{\pi i x_1 x_2} \sum_n g_0(x_2+n) \, e^{2\pi i n x_1}$ is more elementary and amenable to numerical computations, but the commutation relations etc. reveal a richer structure. | |
| Dec 7, 2020 at 4:13 | history | edited | Noam D. Elkies | CC BY-SA 4.0 |
fix sign error in the exponent: exp(-pi*x^2), not exp(pi*x^2) ! Also typo: satisfying, not satisfies
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| Dec 7, 2020 at 4:04 | history | edited | Noam D. Elkies | CC BY-SA 4.0 |
add L^2 connection and Poisson summation
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| Dec 7, 2020 at 3:22 | history | answered | Noam D. Elkies | CC BY-SA 4.0 |