Bounds for spectral projectors on the Euclidean cylinder

Germain, Pierre; Myerson, Simon L. Rydin

doi:10.5802/crmath.378

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2024

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“…For the two-dimensional Euclidean cylinder, the conjecture is identical, and it has been proved with ϵ loss [14]. Finally, this conjecture has also been considered in higher dimensions, for which we refer to [4, 5, 7–10, 15, 16, 18].…”

Section: Introductionmentioning

confidence: 83%

L² to L^p bounds for spectral projectors on the Euclidean two-dimensional torus

Demeter,

Germain

2024

Proceedings of the Edinburgh Mathematical Society

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We consider spectral projectors associated to the Euclidean Laplacian on the two-dimensional torus, in the case where the spectral window is narrow. Bounds for their L2 to Lp operator norm are derived, extending the classical result of Sogge; a new question on the convolution kernel of the projector is introduced. The methods employed include $\ell^2$ decoupling, small cap decoupling and estimates of exponential sums.

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