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 (N,p n ) in such fields K.

DOI : https://doi.org/10.5802/ambp.176
Classification : 40,  46
Mots clés : regular summability methods, M,(N,p n ) methods, product theorems, consistency, analytic functions
@article{AMBP_2003__10_2_261_0,
     author = {P.N. Natarajan},
     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 = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.176/}
}
P.N. Natarajan. 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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.176/

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

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

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

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

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