Intermittent symmetry breaking and stability of the sharp Agmon–Hörmander estimate on the sphere

Negro, Giuseppe; Oliveira e Silva, Diogo

doi:10.1090/proc/16072

Intermittent symmetry breaking and stability of the sharp Agmon–Hörmander estimate on the sphere
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by Giuseppe Negro and Diogo Oliveira e Silva;

Proc. Amer. Math. Soc. 151 (2023), 87-99

DOI: https://doi.org/10.1090/proc/16072

Published electronically: October 19, 2022

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Abstract:

We compute the optimal constant and characterise the maximisers at all spatial scales for the Agmon–Hörmander $L^2$-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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