Tauberian theorem

Etymology
After Austrian and Slovak mathematician (1866-1942).

Noun

 * 1)  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.
 * 2) * 1988, Staff writer, Foreword, [1933, Norbert Wiener, The Fourier Integral and Certain of Its Applications],, 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.
 * 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
describes Tauberian theorems as corrected forms of the false converse of Abelian theorems.

Coordinate terms

 * Abelian theorem