Аннотация:Background: Resonances with binary and few-body decay modes, such as the excited and ground states of neutron- and proton-rich nuclei, are important objects in nuclear physics. However, a description of three- and few-body states in the continuum and their decays, especially in case of the Coulomb interaction, remains a hardly solvable problem.Purpose: We aim to develop an effective technique for finding the parameters of multichannel resonances based on the analysis of discretized spectra without explicitly taking into account boundary conditions.Methods: We introduce a new method for analyzing discretized spectra using spectral and integrated densities of states. For multichannel two-body scattering problems, this approach allows to one calculate a sum of the eigen phase shifts as well as the resonance parameters via solving an eigenvalue problem for the total and asymptotic Hamiltonian matrices in some L2 basis. The generalization of the method to the three-body continuum is used to find the positions and widths of the resonances.Results: We test the presented approach for several multichannel problems and for the three-particle αNN model for light nuclei with A=6. In particular, the width of the 6Be ground state and the parameters of the 3+0 resonance for the 6Li nucleus are found from a diagonalization of the matrix Hamiltonian with realistic interactions on the Gaussian basis.Conclusions: The proposed method can be employed to study three-body decays in nonbinary channels, such as the decay that accompanies two-proton radioactivity.