A THEOREM ON SUMMABILITY FACTORS FOR THE NÖRLUND METHOD FOR DOUBLE SERIES IN ULTRAMETRIC FIELDS

A THEOREM ON SUMMABILITY FACTORS FOR THE NÖRLUND METHOD FOR DOUBLE SERIES IN ULTRAMETRIC FIELDS

P. N. Natarajan

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Abstract

Throughout this paper, K denotes a complete, non-trivially valued, ultrametric (or non-archimedean) eld. 4-dimensional innite matrices, double sequences and double series have entries in K. In this paper, we prove a theorem on summability factors for the Norlund method for double series in K.

Keywords

ultrametric (or non-archimedean) eld, summability factor, double sequence, double series, 4-dimensional innite matrix, regular method, Norlund method.