Linear multiplicative functionals of algebras of S-analytic functions on groups
(Lobachevskii Journal of Mathematics, Volume IX)
Let S be a subsemigroup of a semigroup Σ that generates a group G. We find conditions that assure extendability of linear multiplicative functionals of the algebra AS of S-analytic functions on G with spectra in S to linear multiplicative functionals of the corresponding algebra AΣ. 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 R with spectrum in S, and of the open unit disc in the maximal ideal space of certain subalgebras of H∞ are obtained as corollaries.