Restriction conjecture

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]