Abanin, A. V.; Varziev, V. A. Representing systems of exponential functions in spaces of holomorphic functions with given growth near the boundary. (Russian. English summary) Zbl 1326.30006 Vladikavkaz. Mat. Zh. 14, No. 4, 5-9 (2012). Summary: We consider \((LB)\) spaces of functions which are holomorphic in a convex domain and have a finite type with respect to an order near its boundary. Using Laplace transformation, we give a description of their duals. Then we characterize mimimal absolutely representing systems of exponential functions in these spaces and prove that they always exist. MSC: 30B60 Completeness problems, closure of a system of functions of one complex variable Keywords:spaces of holomorphic functions with a given growth; absolutely representing systems; systems of exponential functions PDFBibTeX XMLCite \textit{A. V. Abanin} and \textit{V. A. Varziev}, Vladikavkaz. Mat. Zh. 14, No. 4, 5--9 (2012; Zbl 1326.30006) Full Text: Link