On Riesz summability factors
Glasgow mathematical journal, Tome 5 (1962) no. 4, pp. 188-196
Voir la notice de l'article provenant de la source Cambridge University Press
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 writeotherwise,and A(w) = AO(w).
On Riesz summability factors. Glasgow mathematical journal, Tome 5 (1962) no. 4, pp. 188-196. doi: 10.1017/S2040618500034572
@misc{10_1017_S2040618500034572,
title = {On {Riesz} summability factors},
journal = {Glasgow mathematical journal},
pages = {188--196},
year = {1962},
volume = {5},
number = {4},
doi = {10.1017/S2040618500034572},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500034572/}
}
[1] 1.Borwein, D., A theorem on Riesz summability, J. London Math. Soc., (2) 31 (1956), 319–324. Google Scholar | DOI
[2] 2.Guha, U. C., Convergence factors for Riesz summability, J. London Math. Soc., (2) 31 (1956), 311–319. Google Scholar | DOI
[3] 3.Hardy, G. H., Divergent series (Oxford, 1949). Google Scholar
[4] 4.Hardy, G. H. and Riesz, M., The general theory of Dirichlet series (Cambridge Tract No. 18, 1915). Google Scholar
[5] 5.de la Vallée Poussin, C.-J., Cours d'analyse infinitésimale (Louvain: Paris, 1921–1922, 4th edn). Google Scholar
Cité par Sources :