Спектр и резольвента одной блочно-операторной матрицы

In the paper the block operator matrix $H$ associated with the system of at most three quantum particles on a $\mathrm{d}$-dimensional lattice is considered. Spectrum of this operator is studied in detail. In particular, it is shown that the operator $H$ has at most four simple eigenvalues lying outside of the essential spectrum. Moreover, the resolvent of $H$ is founded.