Restriction conjecture
From HandWiki
Short description: Conjecture about the behaviour of the Fourier transform on curved hypersurfaces
In harmonic analysis, the restriction conjecture, also known as the Fourier restriction conjecture, is a conjecture about the behaviour of the Fourier transform on curved hypersurfaces.[1][2] It was first hypothesized by Elias Stein.[3] The conjecture states that two necessary conditions needed to solve a problem known as the restriction problem in that scenario are also sufficient.[2][3]
The restriction conjecture is closely related to the Kakeya conjecture, Bochner-Riesz conjecture and the local smoothing conjecture.[4][5]
References
- ↑ Ansede, Manuel (2025-07-14). "What is the smallest space in which a needle can be rotated to point in the opposite direction? This mathematician has finally solved the Kakeya conjecture" (in en-us). https://english.elpais.com/science-tech/2025-07-14/what-is-the-smallest-space-in-which-a-needle-can-be-rotated-to-point-in-the-opposite-direction-this-mathematician-has-finally-solved-the-kakeya-conjecture.html.
- ↑ 2.0 2.1 Kinnear, George (7 February 2011). "Restriction Theory". https://webhomes.maths.ed.ac.uk/gkinnear/files/restriction-talk.pdf.
- ↑ 3.0 3.1 Stedman, Richard James (September 2013). "The Restriction and Kakeya Conjectures". University of Birmingham. https://etheses.bham.ac.uk/id/eprint/5466/1/Stedman14MPhil.pdf.
- ↑ Tao, Terence (2024-11-17). "Terence Tao (@tao@mathstodon.xyz)" (in en). https://mathstodon.xyz/@tao/113496016545909911.
- ↑ Cepelewicz, Jordana (2023-09-12). "A Tower of Conjectures That Rests Upon a Needle" (in en). https://www.quantamagazine.org/a-tower-of-conjectures-that-rests-upon-a-needle-20230912/.
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