Recent progress on the restriction conjecture

By Terence Tao. 2003

59 citations recorded by the source corpus.

The purpose of these notes is describe the state of progress on the restriction problem in harmonic analysis, with an emphasis on the developments of the past decade or so on the Euclidean space version of these problems for spheres and other hypersurfaces. As the field is quite large and has so many applications, it will be impossible to completely survey the field, but we will try to at least give the main ideas and developments in this area. The restriction problem are connected to many other conjectures, notably the Kakeya and Bochner-Riesz conjectures, as well as PDE conjectures such as the local smoothing conjecture. For reasons of space, we will not be able to discuss all these connections in detail; our main focus will be on proving restriction theorems for the Fourier transform.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/40332ec348d4d701a1eeb1b3955818d8981fbf86

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In Applied Mathematics

In Discrete Mathematics and Combinatorics

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Citations in the corpus

Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case (2007, methodology): “For a discussion of recent progress made on this problem, see [17].”
New Restriction Estimates for the 3-d Paraboloid over Finite Fields (2013, background): “We refer the reader to [16] for a more detailed discussion.”
Restriction and spectral multiplier theorems on asymptotically conic manifolds (2010, background): “For more references and new results in this direction, we refer the interested reader to the survey by Tao [38] on the subject.”
Extension theorems for spheres in the finite field setting (2007, unknown): “C A ] 11 D”