Tomographic Fourier extension identities for submanifolds of R n

Jonathan Bennett; Shohei Nakamura; Shobu Shiraki

doi:10.1007/s00029-024-00970-2

Tomographic Fourier extension identities for submanifolds of R n

Jonathan Bennett^*
, Shohei Nakamura
, Shobu Shiraki

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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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
Article number	80
Number of pages	14
Journal	Selecta Mathematica, New Series
Volume	30
DOIs	https://doi.org/10.1007/s00029-024-00970-2
Publication status	Published - 11 Sept 2024

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Tomographic Fourier Extension Identities for Submanifolds of ℝⁿ
Bennett, J., Nakamura, S. & Shiraki, S., 23 Dec 2022, arXiv, 10 p.
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title = "Tomographic Fourier extension identities for submanifolds of R n",

abstract = "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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AU - Nakamura, Shohei

AU - Shiraki, Shobu

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N2 - 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.

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.

UR - http://link.springer.com/journal/29

UR - https://arxiv.org/abs/2212.12348

U2 - 10.1007/s00029-024-00970-2

DO - 10.1007/s00029-024-00970-2

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VL - 30

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

M1 - 80

ER -

Tomographic Fourier extension identities for submanifolds of R n

Abstract

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Tomographic Fourier Extension Identities for Submanifolds of ℝn

Cite this

Tomographic Fourier Extension Identities for Submanifolds of ℝⁿ