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Local maximizers of
adjoint Fourier restriction estimates for the cone,
paraboloid and sphere
Felipe Gonçalves and Giuseppe Negro |
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Vol. 15 (2022), No. 4, 1097–1130
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Abstract |
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We show that, possibly after a compactification of spacetime, constant functions are local maximizers of the Tomas–Stein adjoint Fourier restriction inequality for the cone and paraboloid in every dimension, and for the sphere in dimension up to 60. For the cone and paraboloid we work from the PDE framework, which enables the use of the Penrose and the Lens transformations, which map the conjectured optimal functions into constants. |
Keywords
Fourier extension, Fourier restriction, Schrödinger
equation, wave equation, Strichartz estimates, sharp
inequality, local maximizer, cone, paraboloid
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Mathematical Subject Classification
Primary: 35A23, 42B10, 42B37
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Milestones
Received: 29 March 2020
Revised: 20 October 2020
Accepted: 26 November 2020
Published: 3 September 2022
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Authors |
| Felipe Gonçalves | |
| Hausdorff Center for
Mathematics Universität Bonn Bonn Germany |
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| Giuseppe Negro | |
| Departamento de Matemática Instituto Superior Técnico Lisbon Portugal |
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