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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All labels observed (7)

Label	Occurrences
Riesz means	4
Bochner–Riesz means canonical	2
Bochner–Riesz conjecture	1
Bochner–Riesz conjecture in higher dimensions	1
Bochner–Riesz multipliers	1
Bochner–Riesz problem	1
Dirichlet kernels on compact groups	1

How this entity was disambiguated

This entity first appeared as the object of triple T6716264 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Bochner–Riesz means
Context triple: [Salomon Bochner, notableFor, Bochner–Riesz means]

A. Three regularity results in harmonic analysis
"Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
B. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
"Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
C. Littlewood–Paley theory
Littlewood–Paley theory is a collection of techniques in harmonic analysis that decompose functions into frequency-localized pieces to study their behavior in L^p spaces and related function spaces.
D. Singular Integrals and Differentiability Properties of Functions
"Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
E. Calderón–Zygmund theory
Calderón–Zygmund theory is a branch of harmonic analysis that studies singular integral operators and their boundedness properties on function spaces such as L^p.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Bochner–Riesz means
Target entity description: 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.

A. Three regularity results in harmonic analysis
"Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
B. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
"Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" is a foundational graduate-level textbook by Elias Stein that systematically develops modern harmonic analysis using real-variable techniques, emphasizing singular integrals, Littlewood–Paley theory, and oscillatory integral methods.
C. Littlewood–Paley theory
Littlewood–Paley theory is a collection of techniques in harmonic analysis that decompose functions into frequency-localized pieces to study their behavior in L^p spaces and related function spaces.
D. Singular Integrals and Differentiability Properties of Functions
"Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
E. Calderón–Zygmund theory
Calderón–Zygmund theory is a branch of harmonic analysis that studies singular integral operators and their boundedness properties on function spaces such as L^p.
F. None of above. chosen

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 ⓘ
associatedWith	Bochner–Riesz conjecture ⓘ linked to: Bochner–Riesz means
basedOn	Bochner–Riesz multipliers ⓘ linked to: Bochner–Riesz means
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 ⓘ linked to: Bochner–Riesz means
hasEffect	reducing Gibbs-type oscillations in some settings ⓘ
hasKernel	Bochner–Riesz kernel in physical space ⓘ
hasOpenProblem	Bochner–Riesz conjecture in higher dimensions ⓘ linked to: Bochner–Riesz means
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 ⓘ Salomon Bochner ⓘ
relatedTo	Cesàro means ⓘ Fejér means ⓘ linked to: Fejér’s theorem on Fourier series Littlewood–Paley theory ⓘ Stein–Tomas restriction theorem ⓘ linked to: Fourier restriction theory 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 ⓘ

How these facts were elicited