对称算子I的扩展:内特征函数情况

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2014-03-18 DOI:10.1515/conop-2015-0004
R.T.W. Martin
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引用次数: 6

摘要

给定Hilbert空间上的一个对称线性变换,一个自然要考虑的问题是它的对称扩展集的刻画。这个问题等价于研究固定偏等距的偏等距扩展。通过构造该集合的商与大于或等于θB的所有压缩解析函数φ的集合之间的一个双射,给出了具有有限等指标的对称线性变换B的所有自伴随扩展集和内部Livšic特征函数θB的一个新的函数论刻划。
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Extensions of symmetric operators I: The inner characteristic function case
Abstract Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
期刊最新文献
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