Silvermann-Toeplitz theorem for double sequences and series and its application to Nörlund means in non-archimedean fields

P.N. Natarajan; V. Srinivasan

Annales mathématiques Blaise Pascal (2002)

  • Volume: 9, Issue: 1, page 85-100
  • ISSN: 1259-1734

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Natarajan, P.N., and Srinivasan, V.. "Silvermann-Toeplitz theorem for double sequences and series and its application to Nörlund means in non-archimedean fields." Annales mathématiques Blaise Pascal 9.1 (2002): 85-100. <http://eudml.org/doc/79245>.

@article{Natarajan2002,
author = {Natarajan, P.N., Srinivasan, V.},
journal = {Annales mathématiques Blaise Pascal},
language = {eng},
number = {1},
pages = {85-100},
publisher = {Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal},
title = {Silvermann-Toeplitz theorem for double sequences and series and its application to Nörlund means in non-archimedean fields},
url = {http://eudml.org/doc/79245},
volume = {9},
year = {2002},
}

TY - JOUR
AU - Natarajan, P.N.
AU - Srinivasan, V.
TI - Silvermann-Toeplitz theorem for double sequences and series and its application to Nörlund means in non-archimedean fields
JO - Annales mathématiques Blaise Pascal
PY - 2002
PB - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
VL - 9
IS - 1
SP - 85
EP - 100
LA - eng
UR - http://eudml.org/doc/79245
ER -

References

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  1. [1] G. Bachman, Introduction to p-adic numbers and valuation theory, Academic Press, (1964). Zbl0192.40103MR169847
  2. [2] G.H. Hardy, Divergent series, Oxford (1949). Zbl0032.05801MR30620
  3. [3] Kojima, On the theory of double sequences, Tôhoku Mathematical Journal, 21 (1922), 3-14. Zbl48.0234.04JFM48.0234.04
  4. [4] A.F. Monna, Sur le théorème de Banach-Steinhaus, Indag. Math.25 (1963), 121-131. Zbl0121.32703MR151823
  5. [5] C.N. Moore, On relationships between Nörlund means for double series, Proc. Amer. Math. Soc.5 (1954), 957-963. Zbl0056.28401MR64892
  6. [6] P.N. Natarajan, Criterion for regular matrices in non-archimedean fields, J. Ramanujan Math. Soc.6 (1991), 185-195. Zbl0751.40003MR1132355
  7. [7] P.N. Natarajan, On Nörlund method of summability in non-archimedean fields, J. Analysis2 (1994), 97-102. Zbl0807.40005MR1281500
  8. [8] G.M. Robison, Divergent double sequences and series, Trans. Amer. Math. Soc.28 (1926), 50-73. Zbl52.0223.01MR1501332JFM52.0223.01
  9. [9] V.K. Srinivasan, On certain summation processes in the p-adic field, Indag. Math.27 (1965), 319-325. Zbl0128.28004MR196334

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