On the Criteria of Transversality and Disjointness of Nonnegative Self-Adjoint Extensions of Nonnegative Symmetric Operators

We propose a criterion of transversality and disjointness for the Friedrichs and Krein extensions of a nonnegative symmetric operator in terms of the vectors { φ j , j ϵ 𝕁} that form a Riesz basis of the defect subspace. The criterion is applied to the Friedrichs and Krein extensions of the minimal...

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Bibliographic Details
Published inUkrainian mathematical journal Vol. 70; no. 4; pp. 568 - 580
Main Author Kovalev, Yu. G.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2018
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Criteria
Geometry
Mathematics
Mathematics and Statistics
Operators (mathematics)
Statistics
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Summary:We propose a criterion of transversality and disjointness for the Friedrichs and Krein extensions of a nonnegative symmetric operator in terms of the vectors { φ j , j ϵ 𝕁} that form a Riesz basis of the defect subspace. The criterion is applied to the Friedrichs and Krein extensions of the minimal Schrödinger operator A d with point potentials. We also present a new proof of the fact that the Friedrichs extension of the operator A d is a free Hamiltonian.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-018-1517-9