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arXiv · 2107.14273

Intermittent symmetry breaking and stability of the sharp Agmon--H\"ormander estimate on the sphere

Giuseppe Negro·Diogo Oliveira e Silva
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Abstract

We compute the optimal constant and characterise the maximisers at all spatial scales for the Agmon--H\"ormander $L^2$-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.

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Giuseppe Negro, Diogo Oliveira e Silva. 2021-07-29. Intermittent symmetry breaking and stability of the sharp Agmon--H\"ormander estimate on the sphere. https://arxiv.org/abs/2107.14273

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