Spectra of Elliptic Operators on Quantum Graphs with Small Edges

We consider a general second order self-adjoint elliptic operator on an arbitrary metric graph, to which small graph is glued. This obtained via rescaling given fixed γ by positive parameter ε. The coefficients in the differential expression are varying, and they, as well matrices boundary conditions, can also depend ε we assume that this dependence analytic. introduce special certain extension of has no embedded eigenvalues at threshold its essential spectrum. It known under such assumption perturbed converges limiting operator. Our main results establish convergence spectrum spectral projectors proved well. show converging discrete analytic same true for associated eigenfunctions. provide effective recurrent algorithm determining all Taylor series