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

A. G. Baskakov

Izvestiya. Mathematics , Tome 73 (2009) no. 2, pp. 215-278.

Résumé

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).

Détail

Keywords: linear differential operators, spectrum of an operator, homogeneous spaces of functions, Green function, Fredholm operator.

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