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Tauberian theorems for [J, f(x)] transformations

Published online by Cambridge University Press:  09 April 2009

A. Jakimovski  and
A. Livne
A. Jakimovski
Affiliation:
Tel Aviv University, Israel
A. Livne
Affiliation:
Tel Aviv University, Israel
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Let Σ∞n=0 an(sn=a0+…+an, n≧0) be a series of real or complex numbers. Denote by and two linear transforms T1 and T2 of {sn}. Estimates of the form for sequences {sn} satisfying where {dn} is a certain fixed linear transform of the sequence and depend on the transforms T1, T2 and {dn}, were considered for the first time by Hadwiger [2]. The smallest value of C satisfying (1.2) for all sequences {sn} satisfying (1.3) is known as the Tauberian constant associated with the pair of transforms T1, T2 and {dn}.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 2 , March 1973 , pp. 202 - 221
Copyright
Copyright © Australian Mathematical Society 1973

References

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