对称算子自共轭扩张的酉参数化描述(英文)  

Unitary Parametrization Description of Self-Adjoint Extensions of Symmetric Operators

作　　者：陈金设[1] 孙炯[1] 

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《应用数学》2010年第2期426-437,共12页Mathematica Applicata

基　　金：Supported by National Nature Science Foundation of China(10561005;0861008)

摘　　要：利用构造性的方法,给出了边值空间理论中几个结果新的证明,其中,边值空间理论是有关对称算子自共轭扩张的一种方法.同时,得到了几个新的结果.如发现了一般的边界三元组所具有的结构.进一步地,利用这个结果证明了辅助Hilbert空间H上的酉变换与亏空间K-和K+之间的等距同构映射间存在一个双解析的映射.发现并证明了一般边界条件:B(ψ):=MΓ1ψ+NΓ2ψ=0(其中M,N是阶数为亏指数的方阵)是自共轭的充要条件以及相应的酉变换和边界映射.In this paper,with constructive method,we give new proofs of some results in the theory of boundary value space,which is about the self-adjoint extensions of symmetric operators.Also,we obtain some new results.We discover the structure of a general boundary triplet.With the result,we prove that there is a biholomorphic mapping between the unitary transformations on auxiliary Hilbert space H and the isometric isomorphisms of K-onto K＋,where K±：=ker（A＊iI）,and we obtain the necessary and sufficient condition for the self-adjointness of the boundary conditions B（ψ）：=MΓ1ψ＋NΓ2ψ=0,where M,N are the square matrix with the order equal to the deficiency index,the corresponding unitary transformation and the boundary mappings.

关 键 词：边界映射 对称算子 边界三元组 自共轭扩张 

分 类 号：O177.7[理学—数学]