Spectral analysis of certain non-self-adjoint difference operators (Q789700)

The paper continues the spectral analysis, begun by the author in Ukr. Mat. Zh. 33, 227-233 (1981; Zbl 0464.47026), of the class of (nonselfadjoint) operatos in \(L^ 2(0,1)\) of the fom: \(T=S+V\), where S is the multiplication by the independent variable, \(x\in(0,1+1)\), and V is an integral operator with kernel analytic in both variables in a certain neighborhood of [0,1]. The main result here is a formula for the multiplicity of the eigenvalues of T lying on [0,1]. The relevance of the results to difference operators which are perturbations of selfadjoint ones by matrices with rapidly decreasing off-diagonal elements is pointed out.