Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations

We study linear differential operators with unbounded operator-valued coefficients acting on homogeneous spaces of functions on the semi-axis. We obtain necessary and sufficient conditions for such operators to be invertible or Fredholm. Essential use is made of the spectral theory of difference relations and semigroups of linear relations (multi-valued linear operators)