2018
Том 70
№ 7

All Issues

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

Kovalev Yu. G.


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.

Citation Example: Kovalev Yu. G. On the criteria of transversality and disjointness of nonnegative selfadjoint extensions of nonnegative symmetric operators // Ukr. Mat. Zh. - 2018. - 70, № 4. - pp. 495-505.