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Slicing surfaces and the Fourier restriction conjecture

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  28 May 2009

Fabio Nicola
Fabio Nicola
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy; Email: (fabio.nicola@polito.it)
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Abstract

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We deal with the restriction phenomenon for the Fourier transform. We prove that each of the restriction conjectures for the sphere, the paraboloid and the elliptic hyperboloid in ℝn implies that for the cone in ℝn+1. We also prove a new restriction estimate for any surface in ℝ3 locally isometric to the plane and of finite type.

Keywords

restriction theoremFourier transformconic sections

MSC classification

Secondary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 2 , June 2009 , pp. 515 - 527
Copyright
Copyright © Edinburgh Mathematical Society 2009