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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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Positive linear functionals on group algebras generated by one element

Let $g$ be a group element, let $G$ be the group generated by $g$, and let $\mathbb C G$ be the group algebra on $G$. If we define $\tau:G\to\mathbb C$ as \begin{align*}\tag{1} \tau[g^n]=\begin{cases …