## S. Grigoryan, T. Tonev

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

## (Lobachevskii Journal of Mathematics, Vol.9, pp.29-35)

Let $S$ be a subsemigroup of a semigroup $\S$ 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 $A_\S$.
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 $H^\infty$ are obtained
as corollaries.

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