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arXiv · 1407.3019

Discrete Fourier restriction theorems in two dimensions

John J. F. Fournier
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Abstract

Consider the group ${\mathbb{R}}^2$ with the discrete topology, and denote its Fourier algebra by $A({{\mathbb{R}}_{\rm d}^2})$. We reformulate a theorem of V.A. Yudin as a statement about restrictions of functions in $A({{\mathbb{R}}_{\rm d}^2})$ to the boundary of a strictly convex domain when those functions vanish outside that boundary. We give visual proofs of that statement and a complementary one.

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John J. F. Fournier. 2014-07-11. Discrete Fourier restriction theorems in two dimensions. https://arxiv.org/abs/1407.3019

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