Fourier restriction theory

E792937

branch of harmonic analysis mathematical theory

Fourier restriction theory is a branch of harmonic analysis that studies when and how the Fourier transform of a function can be meaningfully restricted to lower-dimensional subsets such as curves or surfaces.

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Statements (52)

Predicate	Object
instanceOf	branch of harmonic analysis ⓘ mathematical theory ⓘ
aimsTo	characterize boundedness of restriction operators ⓘ obtain sharp Lp estimates for Fourier restriction ⓘ
concerns	how the Fourier transform can be restricted to a subset ⓘ when the Fourier transform can be restricted to a subset ⓘ
context	Euclidean harmonic analysis ⓘ
developedBy	Charles Fefferman NERFINISHED ⓘ Elias M. Stein NERFINISHED ⓘ Jean Bourgain NERFINISHED ⓘ Larry Guth NERFINISHED ⓘ Peter Tomas NERFINISHED ⓘ Terence Tao NERFINISHED ⓘ Thomas Wolff NERFINISHED ⓘ
field	harmonic analysis ⓘ
formalObject	restriction operator of the Fourier transform ⓘ
hasApplication	Schrödinger equation NERFINISHED ⓘ dispersive PDEs ⓘ nonlinear dispersive equations ⓘ wave equation ⓘ
hasProblem	Stein restriction conjecture NERFINISHED ⓘ Tomas–Stein restriction theorem NERFINISHED ⓘ restriction problem for the cone ⓘ restriction problem for the paraboloid ⓘ restriction problem for the sphere ⓘ
relatedTo	Bochner–Riesz problem NERFINISHED ⓘ Kakeya problem NERFINISHED ⓘ Strichartz estimates NERFINISHED ⓘ decoupling theory ⓘ dispersive partial differential equations ⓘ local smoothing estimates ⓘ oscillatory integral operators ⓘ
studies	Fourier transform on curves ⓘ Fourier transform on lower-dimensional subsets ⓘ Fourier transform on surfaces ⓘ restriction of the Fourier transform ⓘ
timePeriod	late 20th century ⓘ
typicalQuestion	for which exponents p and q does the restriction operator extend boundedly from Lp to Lq ⓘ
typicalSubset	cone GENERATED ⓘ curves in Euclidean space GENERATED ⓘ hypersurfaces with nonvanishing curvature GENERATED ⓘ paraboloid GENERATED ⓘ sphere GENERATED ⓘ
usesConcept	Fourier transform ⓘ Lebesgue spaces NERFINISHED ⓘ Littlewood–Paley theory NERFINISHED ⓘ Lp spaces NERFINISHED ⓘ decoupling inequalities ⓘ interpolation theory ⓘ oscillatory integrals ⓘ stationary phase method ⓘ wave packet decomposition ⓘ

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Lawrence Guth → researchInterest → Fourier restriction theory ⓘ