$${{mathbb {R}}^n$ 子漫游的断层傅立叶扩展特性

Selecta Mathematica Pub Date : 2024-09-11 DOI:10.1007/s00029-024-00970-2

Jonathan Bennett, Shohei Nakamura, Shobu Shiraki

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摘要

我们建立了组成 $T_{k,n}(|\widehat{gd\sigma }|^2)$ 的等价性，其中 $g\mapsto \widehat{gd\sigma }$ 是与${\mathbb {R}}^n$ 的一般光滑 k 维子平面相关的傅里叶扩展算子，而 $T_{k,n}$ 是 k 平面变换。本文介绍了与傅里叶限制理论问题的若干联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Tomographic Fourier extension identities for submanifolds of $${\mathbb {R}}^n$$

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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