  Spectral properties of many finite convolution integral operators have been
understood by finding differential operators that commute with them. In this
paper we compile a complete list of such commuting pairs, extending previous
work to complex-valued and non self-adjoint operators. In addition, we
introduce a new kind of commutation relation, which we call sesquicommutation,
that also has implications for the spectral properties of the integral
operator. In this case we also compute a complete list of sequicommuting pairs
of integral and differential operators.
