The story of majorizability as Karamata's condition of convergence for Abel summable series

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Abstract

The greatest Serbian mathematician, Jovan Karamata (1902-1967), gained worldwide fame working on problems related to theorems of a Tauberian nature. His simple and elegant 1930 proof of the Hardy-Littlewood theorem found its place in the well-known monographs by Titchmarsh, Knopp, Doetsch, Widder, Hardy and Favard. It is less known that the method used in this proof was mentioned for the first time at a conference of the Academy of Natural Sciences of the Serbian Royal Academy of Sciences in Belgrade in 1929, where Karamata introduced the notion of majorizability as a new condition of convergence for Abel summable series. This fact holds the key to a historical insight into Karamata's famous proof of the Hardy-Littlewood theorem. © 2009 Elsevier Inc. All rights reserved.

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Nikolić, A. (2009). The story of majorizability as Karamata’s condition of convergence for Abel summable series. Historia Mathematica, 36(4), 405–419. https://doi.org/10.1016/j.hm.2009.06.004

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