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A General Tauberian Condition that Implies Euler Summability

Published online by Cambridge University Press:  20 November 2018

Mangalam R. Parameswaran
Mangalam R. Parameswaran*
Affiliation:
Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2
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Abstract

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Let V be any summability method (whether linear or conservative or not), 0 < p < 1 and s a real or complex sequence. Let Ep denote the matrix of the Euler method. A theorem is proved, giving a condition under which the V-summability of Eps will imply the Ep-summability of s. This extends, in generalized form, an earlier result of N. H. Bingham who considered the case where s is a real sequence and V = B (Borel's method). It is also proved that even for real sequences, the condition given in the theorem cannot be replaced by the condition used by Bingham.

Keywords

Primary: 40G05secondary: 40E99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 3 , 01 September 1994 , pp. 393 - 398
Copyright
Copyright © Canadian Mathematical Society 1994

References

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