Tauberian

 

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Abelian and tauberian theorems

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• tauberian

From Tauber +‎ -ian, specifically referring to Austrian and Slovak mathematician Alfred Tauber (1866-1942).

Tauberian (not comparable)

1. (mathematical analysis) Being or relating to Tauberian theorems, a class of theorems that are partial converses to Abelian theorems.
   • 1992, Dissertation Abstracts International, page 326:

     In the third chapter we obtain characterizations of Tauberian convergence classes in the limiting case and representations of Fourier and Fourier-Stieltjes coefficients.

   • 2003, B. N. Prasad, “1966, Chandigarh - B. N. Prasad”, in The Shaping of Indian Science, Indian Science Congress Association Presidential Addresses, Volume 2: 1948-1981, Universities Press, page 916:

     Lorentz has developed a general method for obtaining Tauberian conditions for absolute summability.

   • 2004, Jacob Korevaar, Tauberian Theory: A Century of Developments, Springer, page 142:

     In this section we use ideas from the proof of Proposition 4.3 to obtain a convergence theorem involving more general Tauberian conditions.

• abelian

•   Divergent series on Wikipedia.Wikipedia
• Tauberian Theorem, Eric W. Weisstein, MathWorld - A Wolfram Web Resource
• G. H. Hardy, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd edition (1999), pages 31 and 46, in which G. H. Hardy states that a Tauberian theorem may be defined as a "corrected form of the false converse of an Abelian theorem."