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Relevant bibliographies by topics / Théorèmes de restriction de Fourier

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Academic literature on the topic 'Théorèmes de restriction de Fourier'

Author: Grafiati

Published: 25 January 2025

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Journal articles on the topic "Théorèmes de restriction de Fourier"

1

Kovač, Vjekoslav. "Fourier restriction implies maximal and variational Fourier restriction." Journal of Functional Analysis 277, no. 10 (2019): 3355–72. http://dx.doi.org/10.1016/j.jfa.2019.03.015.

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2

Demeter, Ciprian, and S. Zubin Gautam. "Bilinear Fourier Restriction Theorems." Journal of Fourier Analysis and Applications 18, no. 6 (2012): 1265–90. http://dx.doi.org/10.1007/s00041-012-9230-9.

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3

Demeter, Ciprian. "Bourgain’s work in Fourier restriction." Bulletin of the American Mathematical Society 58, no. 2 (2021): 191–204. http://dx.doi.org/10.1090/bull/1717.

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4

Kovač, Vjekoslav, and Diogo Oliveira e Silva. "A variational restriction theorem." Archiv der Mathematik 117, no. 1 (2021): 65–78. http://dx.doi.org/10.1007/s00013-021-01604-1.

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AbstractWe establish variational estimates related to the problem of restricting the Fourier transform of a three-dimensional function to the two-dimensional Euclidean sphere. At the same time, we give a short survey of the recent field of maximal Fourier restriction theory.

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5

Shayya, Bassam. "Fourier restriction in low fractal dimensions." Proceedings of the Edinburgh Mathematical Society 64, no. 2 (2021): 373–407. http://dx.doi.org/10.1017/s0013091521000201.

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AbstractLet $S \subset \mathbb {R}^{n}$ be a smooth compact hypersurface with a strictly positive second fundamental form, $E$ be the Fourier extension operator on $S$, and $X$ be a Lebesgue measurable subset of $\mathbb {R}^{n}$. If $X$ contains a ball of each radius, then the problem of determining the range of exponents $(p,q)$ for which the estimate $\| Ef \|_{L^{q}(X)} \lesssim \| f \|_{L^{p}(S)}$ holds is equivalent to the restriction conjecture. In this paper, we study the estimate under the following assumption on the set $X$: there is a number $0 < \alpha \leq n$ such that $|X \cap

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6

Drury, S. W., and B. P. Marshall. "Fourier restriction theorems for degenerate curves." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 3 (1987): 541–53. http://dx.doi.org/10.1017/s0305004100066901.

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Fourier restriction theorems contain estimates of the formwhere σ is a measure on a smooth manifold M in ∝n. This paper is a continuation of [5], which considered this problem for certain degenerate curves in ∝n. Here estimates are obtained for all curves with degeneracies of finite order. References to previous work on this problem may be found in [5].

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7

Bruce, Benjamin Baker. "Fourier restriction to a hyperbolic cone." Journal of Functional Analysis 279, no. 3 (2020): 108554. http://dx.doi.org/10.1016/j.jfa.2020.108554.

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8

Carneiro, Emanuel, Diogo Oliveira e Silva, and Mateus Sousa. "Extremizers for Fourier restriction on hyperboloids." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 36, no. 2 (2019): 389–415. http://dx.doi.org/10.1016/j.anihpc.2018.06.001.

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9

Nicola, Fabio. "Slicing surfaces and the Fourier restriction conjecture." Proceedings of the Edinburgh Mathematical Society 52, no. 2 (2009): 515–27. http://dx.doi.org/10.1017/s0013091507000995.

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AbstractWe 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.

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10

Carbery, Anthony. "Restriction implies Bochner–Riesz for paraboloids." Mathematical Proceedings of the Cambridge Philosophical Society 111, no. 3 (1992): 525–29. http://dx.doi.org/10.1017/s0305004100075599.

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Let Σ ⊆ ℝn be a (compact) hypersurface with non-vanishing Gaussian curvature, with suitable parameterizations, also called Σ: U → ℝn (U open patches in ℝn−1). The restriction problem for Σ is the question of the a priori estimate (for f ∈ S(ℝ))(^denoting the Fourier transform). The Bochner-Riesz problem for Σ is the question of whether the functionsdefine Lp-bounded Fourier multiplier operators on ℝn in the range.

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