Generalized exponential series for distributions (Q1377980)

Absolutely representing systems of generalized exponentials are considered which admit nontrivial expansions of zero in the space \(D_{\beta}'([-a,a]^p)\) of distributions on the \(p\)-dimensional cube \([-a,a]^p .\) The author finds conditions under which the existence of a nontrivial expansion of zero in a system of generalized exponentials \(\mathcal E_{\Lambda} \) that is absolutely convergent in \(D_{\beta}'([-a,a]^p)\) imply that \(\mathcal E_{\Lambda} \) is an absolutely representing system in \(D_{\beta}'([-a,a]^p).\) He also deals with the problem of existence of a continuous linear right inverse of the representation operator associated to an absolutely representing system \(\mathcal E_{\Lambda} \) of generalized exponentials.