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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).

Information

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

References

1.Borwein, D., A theorem on Riesz summability, J. London Math. Soc., (2) 31 (1956), 319–324.CrossRefGoogle Scholar
2.Guha, U. C., Convergence factors for Riesz summability, J. London Math. Soc., (2) 31 (1956), 311–319.CrossRefGoogle Scholar
3.Hardy, G. H., Divergent series (Oxford, 1949).Google Scholar
4.Hardy, G. H. and Riesz, M., The general theory of Dirichlet series (Cambridge Tract No. 18, 1915).Google Scholar
5.de la Vallée Poussin, C.-J., Cours d'analyse infinitésimale (Louvain: Paris, 1921–1922, 4th edn).Google Scholar