On conditions under which the sum of self-adjoint operators with given integer spectra is a scalar operator - Hrushevoi, R. V. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
We describe the set ∑M1 ,...,Mn и of parameters γ for which there exists a decomposition of the operator γIH into a sum of n self-adjoint operators with the spectra belonging to the sets M1 ,...,Mn . The description of this set is performed for Mi = 0,1, ...,ki in the case of n ≥ 4 and in some cases for n = 3.