Tauberian Theorems for Borel-Type Methods of Summability
Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 167-173
Voir la notice de l'article provenant de la source Cambridge University Press
Suppose throughout that s, a n (n=0,1, 2,...) are arbitrary complex numbers, that α>0 and β is real and that N is a non-negative integer such that αN+β≧l. Let where z=x+iy is a complex variable and the power z r is assumed to have its principal value.
Borwein, D.; Smet, E. Tauberian Theorems for Borel-Type Methods of Summability. Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 167-173. doi: 10.4153/CMB-1974-034-1
@article{10_4153_CMB_1974_034_1,
author = {Borwein, D. and Smet, E.},
title = {Tauberian {Theorems} for {Borel-Type} {Methods} of {Summability}},
journal = {Canadian mathematical bulletin},
pages = {167--173},
year = {1974},
volume = {17},
number = {2},
doi = {10.4153/CMB-1974-034-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-034-1/}
}
TY - JOUR AU - Borwein, D. AU - Smet, E. TI - Tauberian Theorems for Borel-Type Methods of Summability JO - Canadian mathematical bulletin PY - 1974 SP - 167 EP - 173 VL - 17 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-034-1/ DO - 10.4153/CMB-1974-034-1 ID - 10_4153_CMB_1974_034_1 ER -
[1] 1. Borwein, D., Relations between Borel-type methods of summability, Journal London Math. Soc, 35 (1960), 65-70. Google Scholar
[2] 2. Borwein, D., On methods of summability based on integral functions II, Proc. Camb. Phil. Soc, 56 (1960), 125-131. Google Scholar
[3] 3. Gaier, D., Zur Frage der Indexverschiebung beim Borel-Verfahren, Math. Zeit, 58 (1953), 453-455. Google Scholar
[4] 4. Hardy, G. H., Divergent series (Oxford, 1949). Google Scholar
Cité par Sources :