On the criteria of transversality and disjointness of nonnegative selfadjoint extensions of nonnegative symmetric operators
We propose criteria of transversality and disjointness for the Friedrichs and Krein extensions of a nonnegative symmetric operator in terms of the vectors $\{ \varphi j , j \in J\}$ that form a Riesz basis of the defect subspace. The criterion is applied to the Friedrichs and Krein extensions of t...
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| Datum: | 2018 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2018
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1571 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We propose criteria of transversality and disjointness for the Friedrichs and Krein extensions of a nonnegative symmetric
operator in terms of the vectors $\{ \varphi j , j \in J\}$ that form a Riesz basis of the defect subspace. The criterion is applied to
the Friedrichs and Krein extensions of the minimal Schr¨odinger operator $\scr A$ d with point potentials. We also present a new
proof of the fact that the Friedrichs extension of the operator $\scr A$ d is a free Hamiltonian. |
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