Pólya's conjecture for Euclidean balls — mentioned by perihelions

Sat, 02 Mar 2024 16:47:38 GMT

What do the eigenfunctions look like? I didn't know the circular disk was such an exotic problem for Laplace's equation. edit: Ah, I misunderstood the problem. The eigenfunctions are exactly solved; the problem of sorting and ordering their eigenvalues is apparently not! From their page 4, - "Although all the eigenvalues of the Dirichlet and Neumann Laplacians on the unit disk are explicitly known in terms of zeros of the Bessel functions or their derivatives, see §2 below, in each case the spectrum is given by a two-parametric family, and rearranging it into a single monotone sequence…

Paper and discussion history. A mention is not an endorsement.

Pólya's conjecture for Euclidean balls — mentioned by VyseofArcadia

Sat, 02 Mar 2024 14:57:21 GMT

arXiv link: https://arxiv.org/abs/2203.07696

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Pólya's conjecture for Euclidean balls · HackerPapers discussions

Pólya's conjecture for Euclidean balls — mentioned by perihelions

Pólya's conjecture for Euclidean balls — mentioned by VyseofArcadia