Tomographic Fourier Extension Identities for Submanifolds of ℝn

Jonathan Bennett; Shohei Nakamura; Shobu Shiraki

doi:10.48550/arXiv.2212.12348

Tomographic Fourier Extension Identities for Submanifolds of ℝⁿ

Mathematics

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Abstract

We establish identities for the composition T_k,n(|gdσˆ|²), where g↦gdσˆ is the Fourier extension operator associated with a general smooth k-dimensional submanifold of ℝⁿ, and T_k,n is the k-plane transform. Several connections to problems in Fourier restriction theory are presented.

Original language	English
Publisher	arXiv
Number of pages	10
DOIs	https://doi.org/10.48550/arXiv.2212.12348
Publication status	Published - 23 Dec 2022

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Tomographic Fourier extension identities for submanifolds of R n
Bennett, J., Nakamura, S. & Shiraki, S., 11 Sept 2024, In: Selecta Mathematica, New Series. 30, 14 p., 80.
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AB - We establish identities for the composition Tk,n(|gdσˆ|2), where g↦gdσˆ is the Fourier extension operator associated with a general smooth k-dimensional submanifold of ℝn, and Tk,n is the k-plane transform. Several connections to problems in Fourier restriction theory are presented.

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Tomographic Fourier Extension Identities for Submanifolds of ℝn

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Tomographic Fourier extension identities for submanifolds of R n

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Tomographic Fourier Extension Identities for Submanifolds of ℝⁿ