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On Nörlund method of summability in non-Archimedean fields. (English) Zbl 0807.40005

V. K. Srinivasan [Nederl. Akad. Wet., Proc., Ser. A 68, 319-325 (1965; Zbl 0128.280)] introduced summation methods in a complete nontrivial valued, non-Archimedean field where he has proved that \(p_ n \to 0\) as \(n \to \infty\) is a sufficient condition for \((N, p_ n)\) to be regular. In this paper the author establishes that the condition is also necessary for regularity. Further he establishes the consistency and equivalence of two Nörlund methods.
Reviewer: I.L.Sukla (Orissa)

MSC:

40J05 Summability in abstract structures
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
12J25 Non-Archimedean valued fields

Citations:

Zbl 0128.280
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