Bochner–Riesz means

E613406

Fourier analysis technique concept in harmonic analysis summability method

Bochner–Riesz means are a family of summability methods in harmonic analysis used to improve the convergence of Fourier series and Fourier integrals by smoothing their partial sums.

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Observed surface forms (1)

Surface form	Occurrences
Riesz means	1

Statements (45)

Predicate	Object
instanceOf	Fourier analysis technique ⓘ concept in harmonic analysis ⓘ summability method ⓘ
appearsIn	dispersive estimates ⓘ partial differential equations ⓘ study of convergence of multiple Fourier series ⓘ
appliesTo	Fourier integrals on Euclidean space ⓘ Fourier series on the torus NERFINISHED ⓘ
associatedWith	Bochner–Riesz conjecture NERFINISHED ⓘ
basedOn	Bochner–Riesz multipliers NERFINISHED ⓘ
contrastedWith	sharp spectral cutoff of partial sums ⓘ
definedOn	Fourier transform side ⓘ
dependsOn	radius parameter in frequency space ⓘ
field	Fourier analysis ⓘ harmonic analysis ⓘ
generalizes	Riesz means NERFINISHED ⓘ
hasEffect	reducing Gibbs-type oscillations in some settings ⓘ
hasKernel	Bochner–Riesz kernel in physical space ⓘ
hasOpenProblem	Bochner–Riesz conjecture in higher dimensions NERFINISHED ⓘ
hasParameter	dimension n ⓘ order parameter δ ⓘ
hasProperty	rotationally symmetric in frequency space ⓘ
improves	norm convergence of Fourier series in some ranges of p and δ ⓘ pointwise convergence of Fourier series in some ranges of p and δ ⓘ
namedAfter	Marcel Riesz NERFINISHED ⓘ Salomon Bochner NERFINISHED ⓘ
relatedTo	Cesàro means ⓘ Fejér means NERFINISHED ⓘ Littlewood–Paley theory NERFINISHED ⓘ Stein–Tomas restriction theorem NERFINISHED ⓘ maximal Bochner–Riesz operator ⓘ spherical summation methods ⓘ square function estimates ⓘ
studiedInContextOf	Lp boundedness of Fourier multipliers ⓘ restriction theory for the Fourier transform ⓘ singular integrals ⓘ
typicalDomain	Rn ⓘ n-dimensional torus ⓘ
usedBy	analysts studying Fourier integrals ⓘ analysts studying Fourier series ⓘ
usedFor	improving convergence of Fourier integrals ⓘ improving convergence of Fourier series ⓘ smoothing partial sums of Fourier integrals ⓘ smoothing partial sums of Fourier series ⓘ
uses	radial cutoff in frequency domain ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Salomon Bochner → notableFor → Bochner–Riesz means ⓘ

Frigyes Riesz → knownFor → Bochner–Riesz means ⓘ

this entity surface form: Riesz means