About: Hardy–Littlewood Tauberian theorem

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In mathematical analysis, the Hardy–Littlewood Tauberian theorem is a Tauberian theorem relating the asymptotics of the partial sums of a series with the asymptotics of its Abel summation. In this form, the theorem asserts that if, as y ↓ 0, the non-negative sequence an is such that there is an asymptotic equivalence then there is also an asymptotic equivalence as n → ∞. The integral formulation of the theorem relates in an analogous manner the asymptotics of the cumulative distribution function of a function with the asymptotics of its Laplace transform.

Attributes	Values
rdfs:label	Taubersatz von Hardy-Littlewood (de) Théorème taubérien de Hardy-Littlewood (fr) Hardy–Littlewood Tauberian theorem (en) 하디-리틀우드 타우버 정리 (ko) Теорема Харди — Литтлвуда (ru)
rdfs:comment	Der Taubersatz von Hardy-Littlewood ist ein mathematischer Satz, der besonders in den Bereichen Funktionentheorie und analytische Zahlentheorie Anwendung findet. Er behandelt ein relativ einfaches Kriterium, mit dem das asymptotische Wachstum einer zahlentheoretischen Funktion aus den Eigenschaften der von ihr erzeugten Funktion bestimmt werden kann. Der Satz ist benannt nach Alfred Tauber und wurde 1914 von den britischen Mathematikern Godfrey Harold Hardy und John Edensor Littlewood bewiesen. 1930 wurde der Beweis von Jovan Karamata wesentlich vereinfacht. (de) En mathématiques, le théorème taubérien de Hardy-Littlewood est un théorème taubérien reliant le comportement asymptotique d'une série à celui de la série obtenue via la méthode de la sommation d'Abel. Ce théorème est nommé en l'honneur de Godfrey Harold Hardy et John Edensor Littlewood qui l'ont démontré en 1914. En 1930, Jovan Karamata en a donné une nouvelle démonstration bien plus simple. (fr) 해석학에서 하디-리틀우드 타우버 정리(영어: Hardy–Littlewood Tauberian theorem)는 어떤 함수의 라플라스 변환의 극한과 함수의 적분의 극한 사이를 연관짓는 타우버 정리이다. (ko) Теорема Харди—Литтлвуда — теорема о свойствах степенных рядов вблизи границы круга сходимости. Доказана Харди и Литтлвудом в 1914 году. (ru) In mathematical analysis, the Hardy–Littlewood Tauberian theorem is a Tauberian theorem relating the asymptotics of the partial sums of a series with the asymptotics of its Abel summation. In this form, the theorem asserts that if, as y ↓ 0, the non-negative sequence an is such that there is an asymptotic equivalence then there is also an asymptotic equivalence as n → ∞. The integral formulation of the theorem relates in an analogous manner the asymptotics of the cumulative distribution function of a function with the asymptotics of its Laplace transform. (en)
dct:subject	Tauberian theorems
Wikipage page ID	22846993 (xsd:integer)
Wikipage revision ID	1083791664 (xsd:integer)
Link from a Wikipage to another Wikipage	Prime number theorem Monomial Jovan Karamata Von Mangoldt function Mathematical analysis G. H. Hardy Gamma function Converse (logic) Slowly varying function Alfred Tauber Cumulative distribution function Abel summation Discontinuity (mathematics) Mathematical proof Abel's theorem Tauberian theorems John Edensor Littlewood Laplace transform Polynomial Integral Real number Series (mathematics) J. E. Littlewood Weierstrass approximation theorem Asymptotic equivalence Asymptotics Tauberian theorem
sameAs	Hardy–Littlewood Tauberian theorem Hardy–Littlewood Tauberian theorem Hardy–Littlewood Tauberian theorem Hardy–Littlewood Tauberian theorem Hardy–Littlewood Tauberian theorem Hardy–Littlewood Tauberian theorem
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Harvtxt dbt:Main dbt:MathWorld dbt:Reflist dbt:Rp
id	t/t092280 (en)
title	Tauberian theorems (en) Hardy-Littlewood Tauberian Theorem (en)
urlname	Hardy-LittlewoodTauberianTheorem (en)
has abstract	Der Taubersatz von Hardy-Littlewood ist ein mathematischer Satz, der besonders in den Bereichen Funktionentheorie und analytische Zahlentheorie Anwendung findet. Er behandelt ein relativ einfaches Kriterium, mit dem das asymptotische Wachstum einer zahlentheoretischen Funktion aus den Eigenschaften der von ihr erzeugten Funktion bestimmt werden kann. Der Satz ist benannt nach Alfred Tauber und wurde 1914 von den britischen Mathematikern Godfrey Harold Hardy und John Edensor Littlewood bewiesen. 1930 wurde der Beweis von Jovan Karamata wesentlich vereinfacht. (de) In mathematical analysis, the Hardy–Littlewood Tauberian theorem is a Tauberian theorem relating the asymptotics of the partial sums of a series with the asymptotics of its Abel summation. In this form, the theorem asserts that if, as y ↓ 0, the non-negative sequence an is such that there is an asymptotic equivalence then there is also an asymptotic equivalence as n → ∞. The integral formulation of the theorem relates in an analogous manner the asymptotics of the cumulative distribution function of a function with the asymptotics of its Laplace transform. The theorem was proved in 1914 by G. H. Hardy and J. E. Littlewood. In 1930, Jovan Karamata gave a new and much simpler proof. (en) En mathématiques, le théorème taubérien de Hardy-Littlewood est un théorème taubérien reliant le comportement asymptotique d'une série à celui de la série obtenue via la méthode de la sommation d'Abel. Ce théorème est nommé en l'honneur de Godfrey Harold Hardy et John Edensor Littlewood qui l'ont démontré en 1914. En 1930, Jovan Karamata en a donné une nouvelle démonstration bien plus simple. (fr) 해석학에서 하디-리틀우드 타우버 정리(영어: Hardy–Littlewood Tauberian theorem)는 어떤 함수의 라플라스 변환의 극한과 함수의 적분의 극한 사이를 연관짓는 타우버 정리이다. (ko) Теорема Харди—Литтлвуда — теорема о свойствах степенных рядов вблизи границы круга сходимости. Доказана Харди и Литтлвудом в 1914 году. (ru)
prov:wasDerivedFrom	wikipedia-en:Hardy–Littlewood_Tauberian_theorem?oldid=1083791664&ns=0
page length (characters) of wiki page	7889 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Hardy–Littlewood_Tauberian_theorem
is Link from a Wikipage to another Wikipage of	Haar's Tauberian theorem Hardy-Littlewood Tauberian theorem Hardy-Littlewood tauberian theorem Hardy–Littlewood tauberian theorem Abelian and Tauberian theorems Littlewood's Tauberian theorem Hardy-Littlewood-Karamata tauberian theorem Hardy–Littlewood–Karamata tauberian theorem Karamata's tauberian theorem Karamata tauberian theorem
is Wikipage redirect of	Hardy-Littlewood Tauberian theorem Hardy-Littlewood tauberian theorem Hardy–Littlewood tauberian theorem Hardy-Littlewood-Karamata tauberian theorem Hardy–Littlewood–Karamata tauberian theorem Karamata's tauberian theorem Karamata tauberian theorem
is foaf:primaryTopic of	wikipedia-en:Hardy–Littlewood_Tauberian_theorem

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