Tomographic Fourier extension identities for submanifolds of Rn

Tomographic Fourier extension identities for submanifolds of Rn

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

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Veröffentlicht in:Selecta mathematica (Basel, Switzerland) Switzerland), 2024, Vol.30 (4)
Hauptverfasser: Bennett, Jonathan, Nakamura, Shohei, Shiraki, Shobu
Format: Artikel
Sprache:eng
Schlagworte:
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
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Zusammenfassung:We establish identities for the composition T k , n ( | g d σ ^ | 2 ) , where g ↦ g d σ ^ is the Fourier extension operator associated with a general smooth k -dimensional submanifold of R n , and T k , n is the k -plane transform. Several connections to problems in Fourier restriction theory are presented.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-024-00970-2