# 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 *A*_{S} of *S*-analytic functions on *G* with spectra in *S* to linear multiplicative functionals of the corresponding algebra *A*_{Σ}. 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.