Summary
Let * denote a convolution with respect to which l 1 becomes a Banach algebra. Necessary and sufficient conditions are given for (l 1, *) 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 Hinčin's factorization theorem is obtained through the use of Delphic semigroups.
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Portions of this work were supported by a Summer Research Fellowship at the University of Missouri-St.Louis
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Schwartz, A.L. l 1-Convolution algebras: Representation and factorization. Z. Wahrscheinlichkeitstheorie verw Gebiete 41, 161–176 (1977). https://doi.org/10.1007/BF00538420
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DOI: https://doi.org/10.1007/BF00538420