Abstract
Let * denote a convolution with respect to which l1 becomes a Banach algebra. Necessary and sufficient conditions are given for (l1, *) to be represented by pointwise products of series of orthogonal polynomials. Properties of the polynomials are related to properties of the convolution; and, in the case of positive convolutions, an analogue of Hincin's factorization theorem is obtained through the use of Delphic semigroups.
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