About: Convergence of Fourier series

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In mathematics, the question of whether the Fourier series of a periodic function converges to a given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics. Convergence is not necessarily given in the general case, and certain criteria must be met for convergence to occur. Determination of convergence requires the comprehension of pointwise convergence, uniform convergence, absolute convergence, Lp spaces, summability methods and the Cesàro mean.

Attributes	Values
rdfs:label	تقارب متسلسلة فورييه (ar) Convergence of Fourier series (en) フーリエ級数の収束 (ja)
rdfs:comment	في الرياضيات، مسألة تقارب متسلسلة فورييه المتعلقة بدالة دورية نحو دالة ما، هي مسألة يبحث عنها في إطار مجال من الرياضيات البحتة يدعى التحليل التناسقي الكلاسيكي. * بوابة رياضيات (ar) In mathematics, the question of whether the Fourier series of a periodic function converges to a given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics. Convergence is not necessarily given in the general case, and certain criteria must be met for convergence to occur. Determination of convergence requires the comprehension of pointwise convergence, uniform convergence, absolute convergence, Lp spaces, summability methods and the Cesàro mean. (en) フーリエ級数の収束（フーリエきゅうすうのしゅうそく）は純粋数学における調和解析の分野で研究される問題である。フーリエ級数は一般には収束するとは限らず、収束するための条件が存在する。収束性の判断には各点収束、一様収束、絶対収束、L p 空間、総和法、チェザロ和の知識を要する。 (ja)
foaf:depiction
dcterms:subject	Fourier series
Wikipage page ID	927236 (xsd:integer)
Wikipage revision ID	1077409513 (xsd:integer)
Link from a Wikipage to another Wikipage	Carleson's theorem Modulus of continuity Bounded variation Almost everywhere Holomorphic function Fourier series Riesz–Fischer theorem Riesz–Thorin theorem Uniform boundedness principle C. R. Acad. Sci. Paris Continuous function Convolution Ann. of Math. Mathematics Measure (mathematics) Salomon Bochner Function (mathematics) Grandi's series Convergent series Andrey Kolmogorov Lennart Carleson Lp space Fejér's theorem Fejér kernel Fundamenta Mathematicae Hardy space Harmonic series (mathematics) Banach space Lecture Notes in Mathematics Acta Math. Dunham Jackson Fourier series Absolutely continuous Banach algebra Norbert Wiener Dirichlet kernel Pointwise convergence Uniform convergence Paul du Bois-Reymond Hilbert space Israel Gelfand Jean-Pierre Kahane Baire category theorem Baire space Andrey Nikolaevich Kolmogorov Absolute convergence Charles Fefferman Lebesgue integration Big O notation Summability kernel Differentiable function Dini test Donald J. Newman Square-integrable If and only if Michael Lacey Christoph Thiele Yitzhak Katznelson Cesàro summation Trigonometric series Wiener algebra Hölder condition Gibbs phenomenon Pure mathematics Periodic function Trigonometric Series Richard Hunt (mathematician) Studia Math. Hölder class Charles Louis Fefferman Summability method Yitzhak Katznelson (mathematician) Sergei Vladimirovich Konyagin Nikolai Lusin
sameAs	Convergence of Fourier series Convergence of Fourier series Convergence of Fourier series Convergence of Fourier series Convergence of Fourier series
dbp:wikiPageUsesTemplate	dbt:Citation_needed dbt:ISBN dbt:Pi dbt:Reflist dbt:Closed-closed
thumbnail	wiki-commons:Special:FilePath/Sawtooth_Fourier_Analysis.jpg?width=300
has abstract	في الرياضيات، مسألة تقارب متسلسلة فورييه المتعلقة بدالة دورية نحو دالة ما، هي مسألة يبحث عنها في إطار مجال من الرياضيات البحتة يدعى التحليل التناسقي الكلاسيكي. * بوابة رياضيات (ar) In mathematics, the question of whether the Fourier series of a periodic function converges to a given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics. Convergence is not necessarily given in the general case, and certain criteria must be met for convergence to occur. Determination of convergence requires the comprehension of pointwise convergence, uniform convergence, absolute convergence, Lp spaces, summability methods and the Cesàro mean. (en) フーリエ級数の収束（フーリエきゅうすうのしゅうそく）は純粋数学における調和解析の分野で研究される問題である。フーリエ級数は一般には収束するとは限らず、収束するための条件が存在する。収束性の判断には各点収束、一様収束、絶対収束、L p 空間、総和法、チェザロ和の知識を要する。 (ja)
prov:wasDerivedFrom	wikipedia-en:Convergence_of_Fourier_series?oldid=1077409513&ns=0

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