Geodesic
Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations
Izvestiya. Mathematics , Tome 73 (2009) no. 2, pp. 215-278

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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).
Keywords: linear differential operators, spectrum of an operator, homogeneous spaces of functions, Green function, Fredholm operator. 
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     author = {A. G. Baskakov},
     title = {Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations},
     journal = {Izvestiya. Mathematics },
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     url = {http://geodesic.mathdoc.fr/item/IM2_2009_73_2_a0/}
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A. G. Baskakov. Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations. Izvestiya. Mathematics , Tome 73 (2009) no. 2, pp. 215-278. http://geodesic.mathdoc.fr/item/IM2_2009_73_2_a0/