Non-archimedean umbral calculus
type: Item
instance of: scholarly article
title: Non-archimedean umbral calculus
zbMATH Open document ID: 0907.46066
author: Ann Verdoodt
published in: Annales Mathématiques Blaise Pascal
publication date: 1998-10-08T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/79198
review text: The famous \textit{K. Mahler's} theorem [J. Reine Angew. Math. 199, 23-34 (1958; Zbl 0080.03504)] states that every continuous function \(f: Z_p\to Q_p\) can be written as \(f(x)= \sum^\infty_{n= 0}a_n\left(\begin{smallmatrix} x\\ n\end{smallmatrix}\right)\), i.e. the functions \(\left(\begin{smallmatrix} x\\ n\end{smallmatrix}\right)\) form a basis of the Banach space \(C(Z_p\to Q_p)\). The present author, basing on his earlier results and on results of L. van Hamme gives constructions of different orthonormal basis for the space \(C(Z_p\to K)\), where \(K\) is a field extension of \(Q_p\), complete with respect to a non-Archimedean absolute value extending the \(p\)-adic absolute value.
Mathematics Subject Classification ID: 46S10
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 05A40
Mathematics Subject Classification ID: 12J25
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 1187665
zbMATH Keywords: basis of the Banach space
zbMATH Keywords: non-Archimedean absolute value
reviewed by: Witold Więsław
MaRDI profile type: Publication
OpenAlex ID: W2094707922
cites work: Q4364140
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DOI: 10.5802/AMBP.105
description: scientific article; zbMATH DE number 1187665