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Generalized exponential series for distributions. (English. Russian original) Zbl 0893.30003
Dokl. Math. 53, No. 2, 266-269 (1996); translation from Dokl. Akad. Nauk 347, No. 6, 739-742 (1996).
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.
Reviewer: F.Haslinger (Wien)
##### MSC:
 30B50 Dirichlet series, exponential series and other series in one complex variable 46A35 Summability and bases in topological vector spaces