Abstract
It is proved that for an [ FC] − group G, the Beurling algebra L ω 1( G) is ∗-regular if and only if ω is non-quasianalytic. As an application the Wiener property is deduced. Further for a σ-compact [ FD] − group G, points in Prim ∗ L ω 1( G) are shown to be spectral provided that ω satisfies Shilov's conditions.
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