Some properties of the \(Y\)-method of summability in complete ultrametric fields (Q699503)

The \(Y\)-method of summability is defined by means of an infinite matrix of the form \(Y=(\alpha^{j}_{i})\), with \(\alpha^{j}_{i}=\lambda_{i-j}\), where \({\lambda_{n}}\) is a bounded sequence in a complete ultrametric field. The paper gives some results regarding the \(Y\)-summability in complete ultrametric fields. One of the \(Y\)-summability results presented in the paper (Theorem 3) in particular illustrates a situation where absolute convergence in classical analysis is effectively replaced by ordinary convergence in non-Archimedian analysis.