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New Tauberian Theorems from Old

Published online by Cambridge University Press:  20 November 2018

Mangalam R. Parameswaran
Mangalam R. Parameswaran*
Affiliation:
Department of Mathematics University of Manitoba Winnipeg, Manitoba R3T2N2
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Abstract

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A new and very general and simple, yet powerful approach is introduced for obtaining new Tauberian theorems for a summability method V from known Tauberian conditions for V, where V is merely assumed to be linear and conservative. The technique yields the known theorems on the weakening of Tauberian conditions due to Meyer-König and Tietz and others and also improves many of them. Several new results are also obtained, even for classical methods of summability, including analogues of Tauber's second theorem for the Borel and logarithmic methods. The approach yields also new Tauberian conditions for the passage from summability by a method V to summability by a method V', as well as to more general methods of summability like absolute summability or summability in abstract spaces; the present paper however confines itself to ordinary summability.

Keywords

40E0540G10Tauberian theorems
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 2 , 01 April 1994 , pp. 380 - 394
Copyright
Copyright © Canadian Mathematical Society 1994

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