2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107651There is a connection between *-representations of algebras associated with graphs and the problem about the spectrum of a sum of Hermitian operators (spectral problem). For algebras associated with extended Dynkin graphs we give an explicit description of the parameters for which there are $*$-representations and an algorithm for constructing these representations.Representation Theory16W10, 16G20, 47L30text