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On Riesz summability factors

Published online by Cambridge University Press:  18 May 2009

D. Borwein  and
B. L. R. Shawyer
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1. Suppose throughout that a, k are positive numbers and that p is the integer such that k—l≦p<k. Suppose also that φ(w), ψ(w) are functions with absolutely continuous (p+1)th derivatives in every interval [a, W] and that φ(w) is positive and unboundedly increasing. Let λ ={λn} be an unboundedly increasing sequence with λ1 > 0.

Given a series and a number m ≧0, we write

otherwise,

and A(w) = AO(w).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 5 , Issue 4 , July 1962 , pp. 188 - 196
Copyright
Copyright © Glasgow Mathematical Journal Trust 1962

References

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