A multiplicative convolution on the spectra of algebras of symmetric analytic functions

We introduce a multiplicative convolution operation in the spectrum of the algebra of symmetric analytic functions of bounded type on the space ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document} that allows us to solve an open question concerning its representation in terms of entire functions of exponential type.