  We consider the algebra of mixed multidimensional integral operators. In
particular, Fredholm integral operators of the first and second kind belongs to
this algebra. For the piecewise constant kernels we provide an explicit
representation of the algebra as a product of simple matrix algebras. This
representation allows us to compute the inverse operators (or to solve the
corresponding integral equations) and to find the spectrum explicitly.
Moreover, explicit traces and determinants are also constructed. So, roughly
speaking, the analysis of integral operators is reduced to the analysis of
matrices. All the qualitative characteristics of the spectrum are preserved
since only the kernels are approximated.
