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Scientific reports of Bukhara State University

Article Title

DESCRIPTION OF THE SPECTRUM OF A QUADRATIC OPERATOR MATRIX OF ORDER 4

Abstract

In the paper a quadratic block operator matrix of order acting in the zero-, one-, two- and three-particle subspaces of the Fock space has been considered. The essential spectrum of the matrix is described via the spectrum of the corresponding quadratic operator matrix of order . It has been proved that the essential spectrum of consists union of at most seven bounded closed intervals.