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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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