Linear differential operators invertible in an integro-differential sense

The talk discusses linear differential operators with one independent variable that are invertible with the inverse operators being integro-differential ones. Namely, the inverse operators are compositions of invertible differential operators and diagonal operators with unities and integrals on the diagonal. An algorithm for checking invertibility in the above sense is presented. The results are generalized to the C-differential operators on the infinitely prolonged evolution equation with one independent variable.