  An isometric operator V in a Pontryagin space H is called standard, if its
domain and the range are nondegenerate subspaces in H. A description of
coresolvents for standard isometric operators is known and basic underlying
concepts that appear in the literature are unitary colligations and
characteristic functions. In the present paper generalized coresolvents of
non-standard Pontryagin space isometric operators are described. The methods
used in this paper rely on a new general notion of boundary pairs introduced
for isometric operators in a Pontryagin space setting. Even in the Hilbert
space case this notion generalizes the earlier concept of boundary triples for
isometric operators and offers an alternative approach to study operator valued
Schur functions without any additional invertibility requirements appearing in
the ordinary boundary triple approach.
