Convolution of Nörlund methods in non-archimedean fields. (English) Zbl 0919.46056

Summary: We obtain a few inclusion theorems for the convolution of Nörlund methods in the form \((N,r_n) \subseteq (N,p_n)* (N,q_n)\) in complete, nontrivially valued, non-archimedean fields.


46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
46A45 Sequence spaces (including Köthe sequence spaces)
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Full Text: DOI Numdam EuDML


[1] Bachman, G., Introduction to p-adic numbers and valuation theory, Academic Press, 1964. · Zbl 0192.40103
[2] Monna, A.F., Sur le théorème de Banach-Steinhaus, Indag. Math.25 (1963), 121-131. · Zbl 0121.32703
[3] Natarajan, P.N., Multiplication of series with terms in a non-archimedean field, Simon Stevin52 (1978), 157-160. · Zbl 0393.40006
[4] Natarajan, P.N., Criterion for regular matrices in non-archimedean fields, J. Ramanujan Math. Soc.6 (1991), 185-195. · Zbl 0751.40003
[5] Natarajan, P.N., On Nörlund method of summability in non-archimedean fields, J. Analysis2 (1994), 97-102. · Zbl 0807.40005
[6] Russell, D.C., Convolution of Nörlund summability methods, Proc. London Math. Soc.9 (1959), 1-20. · Zbl 0089.03902
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.