论文标题
在蓬蒂古蛋白空间和广义核心中的等距运算符的单一边界对
Unitary boundary pairs for isometric operators in Pontryagin spaces and generalized coresolvents
论文作者
论文摘要
如果pontryagin空间H中的等距运算符v被称为标准，如果其域和范围是H中的非排定子空间。标准等级操作员的内核的描述是已知的，并且文献中出现的基本基础概念是单位胶合物和特征性的功能。在本文中，描述了非标准的蓬松素空间等距运算符的广义核心。本文中使用的方法依赖于在Pontryagin空间设置中引入的用于等距运算符的新的一般边界对概念。即使在希尔伯特（Hilbert）空间案例中，这个概念也概括了等距运算符的边界三元组概念，并提供了一种替代方法来研究操作员有价值的Schur函数，而在普通边界三重方法中出现了任何其他可逆性要求。
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.
