Intermittent symmetry breaking and stability of the sharp Agmon--H\"ormander estimate on the sphere
Classical Analysis and ODEs
2022-03-14 v2 Analysis of PDEs
Abstract
We compute the optimal constant and characterise the maximisers at all spatial scales for the Agmon--H\"ormander -Fourier adjoint restriction estimate on the sphere. The maximisers switch back and forth from being constants to being non-symmetric at the zeros of two Bessel functions. We also study the stability of this estimate and establish a sharpened version in the spirit of Bianchi--Egnell. The corresponding stability constant and maximisers again exhibit a curious intermittent behaviour.
Keywords
Cite
@article{arxiv.2107.14273,
title = {Intermittent symmetry breaking and stability of the sharp Agmon--H\"ormander estimate on the sphere},
author = {Giuseppe Negro and Diogo Oliveira e Silva},
journal= {arXiv preprint arXiv:2107.14273},
year = {2022}
}
Comments
14 pages, 2 figures. Referee suggestions incorporated. To appear in Proceedings of the American Mathematical Society