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Tauberian theorem

Tauberian theorem noun: 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.

Noun

Tauberian theorem (plural Tauberian theorems)

  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.
    • Paragraph five deals with (A*)-algebras and contains a proof of a vector-valued variant of Wiener's Tauberian theorem.1957, Einar Hille, Ralph Saul Phillips, Functional Analysis and Semi-groups, Part 1, American Mathematical Society, page 117
    • 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...1988, Staff writer, Foreword, [1933, Norbert Wiener, The Fourier Integral and Certain of Its Applications], Cambridge University Press, 1988 reissue, page xi

Forms of Tauberian theorem

pluralTauberian theorems
alternative formtauberian theorem

Origin of Tauberian theorem

After Austrian and Slovak mathematician Alfred Tauber (1866-1942).

Questions about Tauberian theorem

What does Tauberian theorem mean?
Tauberian theorem means 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.
What part of speech is Tauberian theorem?
Tauberian theorem is a noun.
What is the plural of Tauberian theorem?
The plural of Tauberian theorem is Tauberian theorems.

Words near Tauberian theorem in the dictionary

  1. taubada
  2. taubadas
  3. Tauber
  4. Tauberbischofsheim
  5. tauberian
  6. Tauberian theorem
  7. Tauberian theorems
  8. Taubers
  9. Taubes
  10. Taubeses
  11. Taubin

Source and license

Adapted from Wiktionary: Tauberian theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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