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Linear multiplicative functionals of algebras of \(S\)-analytic functions on groups. (English) Zbl 1017.46032
Summary: Let \(S\) be a subsemigroup of a semigroup \(S\) that generates a group \(\Sigma\). We find conditions that assure extendability of linear multiplicative functionals of the algebra \(A_S\) of \(S\)-analytic functions on \(G\) with spectra in \(S\) to linear multiplicative functionals of the corresponding algebra \(A_\Sigma\). Conditions for existence of dense homeomorphic embeddings of the upper half plane in the maximal ideal space of the algebra of almost periodic functions on \(\mathbb{R}\) with spectrum in \(S\), and of the open unit disc in the maximal ideal space of certain subalgebras of \(H^\infty\) are obtained as corollaries.
MSC:
46J20 Ideals, maximal ideals, boundaries
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