Abstract
The approach herein investigates a topological algebra setting with translation so that Tauberian results are possible, although not necessarily accompanied by the general analytic function theorems usually associated with the L1 group algebra. Accordingly, the exposition is preliminary for topological algebra generalizations of the known results in spectral synthesis by Malliavin, Kahane, Katznelson, Varopoulous, and Warner. The Tauberian remarks are anticipatory for an appropriate Malliavin lemma guaranteeing the existence of a e L1, b e L∞, related by specific properties of certain support sets, and such that ∫ ab≠ 0; correspondingly, an investigation of S sets will follow.
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