Product Theorems for Certain Summability Methods in Non-archimedean Fields
Annales Mathématiques Blaise Pascal, Tome 10 (2003) no. 2, pp. 261-267.

In this paper, $K$ denotes a complete, non-trivially valued, non-archimedean field. Sequences and infinite matrices have entries in $K.$ The main purpose of this paper is to prove some product theorems involving the methods $M$ and $\left(N,{p}_{n}\right)$ in such fields $K.$

DOI : https://doi.org/10.5802/ambp.176
Classification : 40,  46
Mots clés : regular summability methods, $M,\left(N,{p}_{n}\right)$ methods, product theorems, consistency, analytic functions
@article{AMBP_2003__10_2_261_0,
author = {Natarajan, P.N.},
title = {Product Theorems for Certain Summability Methods in Non-archimedean Fields},
journal = {Annales Math\'ematiques Blaise Pascal},
pages = {261--267},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {10},
number = {2},
year = {2003},
doi = {10.5802/ambp.176},
mrnumber = {2031271},
zbl = {1049.40006},
language = {en},
url = {http://www.numdam.org/articles/10.5802/ambp.176/}
}
Natarajan, P.N. Product Theorems for Certain Summability Methods in Non-archimedean Fields. Annales Mathématiques Blaise Pascal, Tome 10 (2003) no. 2, pp. 261-267. doi : 10.5802/ambp.176. http://www.numdam.org/articles/10.5802/ambp.176/

[1] Escassut, A. Analytic elements in $p$-adic Analysis, World Scientific Publishing Co., 1995 | MR 1370442 | Zbl 0933.30030

[2] Monna, A.F. Sur le théorème de Banach-Steinhaus, Indag. Math., Volume 25 (1963), pp.  121-131 | MR 151823 | Zbl 0121.32703

[3] Natarajan, P.N. Multiplication of series with terms in a non-archimedean field, Simon Stevin, Volume 52 (1978), pp.  157-160 | MR 524352 | Zbl 0393.40006

[4] Natarajan, P.N. On Nörlund method of summability in non-archimedean fields, J.Analysis, Volume 2 (1994), pp.  97-102 | MR 1281500 | Zbl 0807.40005

[5] Natarajan, P.N.; Srinivasan, V Silvermann-Toeplitz theorem for double sequences and series and its application to Nörlund means in non-archimedean fields, Ann.Math. Blaise Pascal, Volume 9 (2002), pp.  85-100 | Article | Numdam | MR 1914263 | Zbl 1009.40002

[6] Srinivasan, V.K. On certain summation processes in the $p$-adic field, Indag. Math., Volume 27 (1965), pp.  368-374 | MR 196334 | Zbl 0128.28004