Restriction conjecture

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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

  1. ↑ 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". EL PAÍS English. Retrieved 2025-07-20.
  2. 1 2 Kinnear, George (7 February 2011). "Restriction Theory" (PDF). webhomes.maths.ed.ac.uk.
  3. 1 2 Stedman, Richard James (September 2013). "The Restriction and Kakeya Conjectures" (PDF). University of Birmingham.
  4. ↑ Tao, Terence (2024-11-17). "Terence Tao (@tao@mathstodon.xyz)". Mathstodon. Retrieved 2025-07-20.
  5. ↑ Cepelewicz, Jordana (2023-09-12). "A Tower of Conjectures That Rests Upon a Needle". Quanta Magazine. Retrieved 2025-07-20.


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