In this paper, denotes a complete, non-trivially valued, non-archimedean field. Sequences and infinite matrices have entries in The main purpose of this paper is to prove some product theorems involving the methods and in such fields
Mots clés : regular summability methods, $M,(N,p_n)$ 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}, zbl = {1049.40006}, mrnumber = {2031271}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ambp.176/} }
TY - JOUR AU - Natarajan, P.N. TI - Product Theorems for Certain Summability Methods in Non-archimedean Fields JO - Annales mathématiques Blaise Pascal PY - 2003 SP - 261 EP - 267 VL - 10 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.176/ DO - 10.5802/ambp.176 LA - en ID - AMBP_2003__10_2_261_0 ER -
%0 Journal Article %A Natarajan, P.N. %T Product Theorems for Certain Summability Methods in Non-archimedean Fields %J Annales mathématiques Blaise Pascal %D 2003 %P 261-267 %V 10 %N 2 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.176/ %R 10.5802/ambp.176 %G en %F AMBP_2003__10_2_261_0
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] Analytic elements in -adic Analysis, World Scientific Publishing Co., 1995 | MR | Zbl
[2] Sur le théorème de Banach-Steinhaus, Indag. Math., Volume 25 (1963), pp. 121-131 | MR | Zbl
[3] Multiplication of series with terms in a non-archimedean field, Simon Stevin, Volume 52 (1978), pp. 157-160 | MR | Zbl
[4] On Nörlund method of summability in non-archimedean fields, J.Analysis, Volume 2 (1994), pp. 97-102 | MR | Zbl
[5] 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 | DOI | Numdam | MR | Zbl
[6] On certain summation processes in the -adic field, Indag. Math., Volume 27 (1965), pp. 368-374 | MR | Zbl
Cité par Sources :