Tauberian theorem

== English == === Alternative forms === tauberian theorem === Etymology === After Austrian and Slovak mathematician Alfred Tauber (1866-1942). === Noun === Tauberian theorem (plural Tauberian theorems) (mathematical analysis) Any of a class of theorems which, for a given Abelian theorem, specifies conditions such that any series whose Abel sums converge (as stipulated by the Abelian theorem) is in fact convergent. 1988, Staff writer, Foreword, [1933, Norbert Wiener, The Fourier Integral and Certain of Its Applications], Cambridge University Press, 1988 reissue, page xi, Not only did the general Tauberian theorem give a unifying view on questions involving summations and limits, but it introduced a paradigm for what was called abstract harmonic analysis a few years later. […] Generalized harmonic analysis is the subject-matter of the last chapter, though it was conceived before the Tauberian theorems. ==== Usage notes ==== G. H. Hardy describes Tauberian theorems as corrected forms of the false converse of Abelian theorems. ==== Coordinate terms ==== Abelian theorem === References === === Further reading === Divergent series on Wikipedia.Wikipedia Hardy–Littlewood tauberian theorem on Wikipedia.Wikipedia Tauberian Theorem, Eric W. Weisstein, MathWorld - A Wolfram Web Resource