Dudko A. Finite-dimensional spectral problems on graphs

The dissertation is devoted to problems describing small transverse oscillations of graphs whose edges are Stieltjesian strings, that is, weightless elastic threads carrying a finite number of point masses (beads, in M.G. Crane's terminology). The same, from the point of view of mathematics, finite-dimensional spectral problems describe longitudinal oscillations of graphs, the edges of which consist of point masses connected by springs. This topic is a finite-dimensional analogue of the so-called quantum graph theory, which studies spectral problems generated by the differential equations of quantum mechanics defined on graphs.This dissertation work is theoretical in nature, so its results are of interest in the field of mathematical physics, differential and difference equations and their applications. They can also be used in the theory of the synthesis of electrical circuits.