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arXiv · 2212.12348

Tomographic Fourier Extension Identities for Submanifolds of $\mathbb{R}^n$

Jonathan Bennett·Shohei Nakamura·Shobu Shiraki
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Abstract

We establish identities for the composition $T_{k,n}(|\widehat{gd\sigma}|^2)$, where $g\mapsto \widehat{gd\sigma}$ is the Fourier extension operator associated with a general smooth $k$-dimensional submanifold of $\mathbb{R}^n$, and $T_{k,n}$ is the $k$-plane transform. Several connections to problems in Fourier restriction theory are presented.

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Jonathan Bennett, Shohei Nakamura, Shobu Shiraki. 2022-12-23. Tomographic Fourier Extension Identities for Submanifolds of $\mathbb{R}^n$. https://arxiv.org/abs/2212.12348

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