  In this paper we study generalized J-inner matrix valued functions which
appear as resolvent matrices in various indefinite interpolation problems.
Reproducing kernel indefinite inner product spaces associated with a
generalized J-inner matrix valued function W are studied and intensively used
in the description of the range of the linear fractional transformation
associated with W and applied to the Schur class. For a subclass of generalized
J-inner matrix valued function W the notion of associated pair is introduced
and factorization formulas for W are found.
