On Riesz Bases of Eigenfunctions of Integral Operators with Kernels Discontinuous on Diagonals

Riesz bases of eigenfunctions of integral operators with kernels discontinuous on diagonals are considered. Operator and integral operators of more general form, whose kernels are allowed to have discontinuities, are also considered. The vanishing of the range of operator at x = 0 makes it possible to prove the basis property under only one additional requirement. The operator A to an operator on the space of vector-functions of dimension 2 is considered. For any finite set of integers sufficiently large in absolute value, all characteristic numbers of the operator A sufficiently large in absolute value are prime.