On the criteria of transversality and disjointness of nonnegative selfadjoint extensions of nonnegative symmetric operators

  • Yu. G. Kovalev

Abstract

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.
Published
25.04.2018
How to Cite
KovalevY. G. “On the Criteria of Transversality and Disjointness of Nonnegative selfadjoint extensions of Nonnegative Symmetric Operators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 4, Apr. 2018, pp. 495-0, http://umj.imath.kiev.ua/index.php/umj/article/view/1571.
Section
Research articles