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In [[mathematics]], '''Littlewood's Tauberian theorem''' is a strengthening of [[Tauber's theorem]] introduced by {{harvs {{harvtxt|Littlewood|1953}} described his discovery of the proof of his Tauberian theorem. [[Alfred Tauber]]'s original theorem was similar to Littlewood's, ...

==Abelian and Tauberian theorem== [[Tauberian theorem]]: Suppose that <math>\sum_{n=1}^\infty a_n</math> is Lambert summa ...

...thematical analysis]], the '''Hardy–Littlewood Tauberian theorem''' is a [[Tauberian theorem]] relating the [[asymptotics]] of the partial sums of a [[series (m {{main|Littlewood's Tauberian theorem}} ...

.... It is related to the [[integral]] formulation of the [[Hardy–Littlewood Tauberian theorem]]. [[Category:Tauberian theorems]] ...

...e102/lectures/Laplace_Transform/node17.html |title=Initial and Final Value Theorems |first=Ruye |last=Wang |date=2010-02-17 |accessdate=2011-10-21 |archive-dat Conversely, a Tauberian final value theorem makes assumptions about the frequency-domain behaviour ...

*[[Hardy–Littlewood tauberian theorem]] and its treatment by Karamata [[Category:Tauberian theorems]] ...

{{main|Wiener tauberian theorem}} * {{Citation | last=Wiener|first=Norbert|title=Tauberian Theorems|journal=Annals of Mathematics|volume=33|issue=1|year=1932|pages=1&ndash;100 ...

...rem,<ref>{{cite journal |last=Wiener |first=N. |year=1932 |title=Tauberian Theorems |journal=[[Annals of Mathematics]] |volume=33 |issue=1 |pages=1–100 |jstor= [[Category:Theorems in Fourier analysis]] ...

...ifford John Earle Jr.|Clifford John Earle, Jr.]] with thesis ''An integral Tauberian theorem and other topics''.<ref>{{MathGenealogy|id=17256}}</ref> After that *Tauberian theorems and slowly varying functions . Trans. Amer. Math. Soc. 133 (1968) 333–356. ...

...| last2=Zhiboedov | first2=Alexander | title=Modular invariance, tauberian theorems and microcanonical entropy | journal=Journal of High Energy Physics | publi ...

...shed it in 1936.{{r|de1}} Their original proof used the [[Hardy–Littlewood Tauberian theorem]]; later, they published another, elementary proof.{{r|de2}} [[Category:Theorems in number theory]] ...

{{defn|1=[[Cartan's theorems A and B]].}} {{term|Tauberian}} ...