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 in:Ukrainian mathematical journal 2018-09, Vol.70 (4), p.568-580
Main Author: Kovalev, Yu. G.
Format: Article
Language:English
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