The topological dual of the space \(B^ q\) of \(q\)-almost-even-number-theoretical functions \((0<q<\infty))\)
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 \(q=1\).
\(q\)-almost-even number-theoretical functions
scientific article; zbMATH DE number 4087768