Tauberian theorems for the \((\overline N, p_{m,n})\) and \((M, \lambda_{m,n})\) methods for double series over ultrametric fields

DOI10.1134/S2070046618020036zbMath1414.40006OpenAlexW2800130354MaRDI QIDQ1616626

P. N. Natarajan

Publication date: 7 November 2018

Published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s2070046618020036

zbMATH Keywords

double seriesTauberian theoremdouble sequenceregular matrixnon-Archimedean fieldweighted mean method\((M, \lambda_{m,n})\) method

Mathematics Subject Classification ID

Sequence spaces (including Köthe sequence spaces) (46A45) Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Multiple sequences and series (40B05) Tauberian theorems (40E05) Non-Archimedean analysis (26E30)

Cites Work

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• Silvermann-Toeplitz theorem for double sequences and series and its application to Nőrlund means in non-Archimedean fields
• A Tauberian theorem for weighted means in non-Archimedean fields
• Product theorems for certain summability methods in non-Archimedean fields
• An introduction to ultrametric summability theory
• A Tauberian Theorem for Weighted Means in Non-Archimedean Fields - Revisited and Revised