The topological dual of the space \(B^ q\) of \(q\)-almost-even-number-theoretical functions \((0<q<\infty))\)
type: Item
instance of: scholarly article
title: The topological dual of the space \(B^ q\) of \(q\)-almost-even-number-theoretical functions \((0<q<\infty))\)
zbMATH Open document ID: 0665.10031
DOI: 10.1007/BF01199815
author: Peter Kunth
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: First, the topological dual space of the complex \(B^ q\)-Fréchet-space of ``\(q\)-almost-even number-theoretical functions'' \((0<q<\infty)\) is determined by using an \(L^ q\)-isomorphism-theorem of J. Knopfmacher. As a corollary some multiplication properties of \(B^ 1\)- and \(B^{\infty}\)-functions are given, which complement well-known results about \(B^ q\)-functions \((1<q<\infty).\) In the second part of the study, the dual of \(B^ q\) for \(1<q<\infty\) is calculated ``directly'', i.e. without applying the \(L^ q\)-theory; this is done, similarly, for \(q=1\).
Mathematics Subject Classification ID: 11N99
Mathematics Subject Classification ID: 46A20
Mathematics Subject Classification ID: 11K65
zbMATH DE Number: 4087768
zbMATH Keywords: dual space
zbMATH Keywords: \(B^ q\)-Fréchet-space
zbMATH Keywords: \(q\)-almost-even number-theoretical functions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4087768