About a structure of exponential monomials on some locally compact abelian groups

S. S. Platonov

Problemy analiza, Tome 1 (2012) no. 1, pp. 3-14

Résumé

We describe the structure of some class of exponential monomials on some locally compact abelian groups. The main result of the paper is the next theorem. Let $\tilde{G}$ and $G$ be locally compact abelian groups, $\alpha : \tilde{G}\to G$ be a continuous surjective homomorphism and $H$ be a kernel of $\alpha$. If $\alpha$ is a an open maps from $\tilde{G}$ to $G$ then any exponential monomial $\Phi(t)$ on the group $\tilde{G}$, which satisfy the condition $\Phi(t+h)=\Phi(t)\forall h\in H, t\in \tilde{G}$, can be presented in the form $\Phi(t)=f(\alpha(t))$ for some exponential monomial $f(x)$ on the group $G$.