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

Abstract

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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 .

How to cite

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Natarajan, 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

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

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