# Product Theorems for Certain Summability Methods in Non-archimedean Fields

P.N. Natarajan^{[1]}

- [1] Ramakrishna Mission Vivekananda College Department of Mathematics Mylapore Chennai 600 004 INDIA

Annales mathématiques Blaise Pascal (2003)

- Volume: 10, Issue: 2, page 261-267
- ISSN: 1259-1734

## Access Full Article

top## Abstract

top## How to cite

topNatarajan, P.N.. "Product Theorems for Certain Summability Methods in Non-archimedean Fields." Annales mathématiques Blaise Pascal 10.2 (2003): 261-267. <http://eudml.org/doc/10489>.

@article{Natarajan2003,

abstract = {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 $K.$},

affiliation = {Ramakrishna Mission Vivekananda College Department of Mathematics Mylapore Chennai 600 004 INDIA},

author = {Natarajan, P.N.},

journal = {Annales mathématiques Blaise Pascal},

keywords = {regular summability methods; $M,(N,p_n)$ methods; product theorems; consistency; analytic functions; non-Archimedian field; summability method; product theorem; regular method},

language = {eng},

month = {7},

number = {2},

pages = {261-267},

publisher = {Annales mathématiques Blaise Pascal},

title = {Product Theorems for Certain Summability Methods in Non-archimedean Fields},

url = {http://eudml.org/doc/10489},

volume = {10},

year = {2003},

}

TY - JOUR

AU - Natarajan, P.N.

TI - Product Theorems for Certain Summability Methods in Non-archimedean Fields

JO - Annales mathématiques Blaise Pascal

DA - 2003/7//

PB - Annales mathématiques Blaise Pascal

VL - 10

IS - 2

SP - 261

EP - 267

AB - 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 $K.$

LA - eng

KW - regular summability methods; $M,(N,p_n)$ methods; product theorems; consistency; analytic functions; non-Archimedian field; summability method; product theorem; regular method

UR - http://eudml.org/doc/10489

ER -

## References

top- A. Escassut, Analytic elements in $p$-adic Analysis, (1995), World Scientific Publishing Co. Zbl0933.30030MR1370442
- A.F. Monna, Sur le théorème de Banach-Steinhaus, Indag. Math. 25 (1963), 121-131 Zbl0121.32703MR151823
- P.N. Natarajan, Multiplication of series with terms in a non-archimedean field, Simon Stevin 52 (1978), 157-160 Zbl0393.40006MR524352
- P.N. Natarajan, On Nörlund method of summability in non-archimedean fields, J.Analysis 2 (1994), 97-102 Zbl0807.40005MR1281500
- 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 9 (2002), 85-100 Zbl1009.40002MR1914263
- V.K. Srinivasan, On certain summation processes in the $p$-adic field, Indag. Math. 27 (1965), 368-374 Zbl0128.28004MR196334

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.