On conditions under which the sum of self-adjoint operators with given integer spectra is a scalar operator

We describe the set of parameters γ for which there exists a decomposition of the operator γI _H in a sum of n self-adjoint operators with spectra from the sets M ₁, …, M _n, M _i = 0, 1, …, k _i, for n ≥ 4 and, in some cases, for n = 3. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 4, pp. 470–477, April, 2008.