An isometric operator V in a Pontryagin space \({{{\mathfrak {H}}}}\) is called standard, if its domain and the range are nondegenerate subspaces in \({{{\mathfrak {H}}}}\). 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.

如果Pontryagin空间\（{{{\ mathfrak {H}}}} \}中的等距算子V的标准域和范围是\（{{{\ mathfrak {H}}}}中的非退化子空间，则称其为标准\）。对于标准等距算符的核心溶剂的描述是已知的，并且在文献中出现的基本基本概念是单数和特征函数。在本文中，描述了非标准Pontryagin空间等距算符的广义核溶剂。本文中使用的方法依赖于为Pontryagin空间设置中的等距算符引入边界对的新通用概念。即使在希尔伯特空间案例中，该概念也为等距算符推广了较早的边界三元组概念，并提供了一种研究算子值Schur函数的替代方法，而普通的边界三元组方法中没有任何其他可逆性要求。