Linear multiplicative functionals of algebras of S-analytic functions on groups

Abstract

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 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.