N. Goloshchapova

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Articles: 2

On the extremal extensions of a non-negative Jacobi operator

Aleksandra Ananieva, Nataly Goloshchapova

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 19 (2013), no. 4, 310-318

We consider the minimal non-negative Jacobi operator with $p\times p-$matrix entries. Using the technique of boundary triplets and the corresponding Weyl functions, we describe the Friedrichs and Krein extensions of the minimal Jacobi operator. Moreover, we parametrize the set of all non-negative extensions in terms of boundary conditions.

Multi-dimensional Schrödinger operators with point interactions

Nataly Goloshchapova

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 17 (2011), no. 2, 126-143

We study two- and three-dimensional matrix Schrödinger operators with $m\in \Bbb N$ point interactions. Using the technique of boundary triplets and the corresponding Weyl functions, we complete and generalize the results obtained by the other authors in this field. For instance, we parametrize all self-adjoint extensions of the initial minimal symmetric Schrödinger operator by abstract boundary conditions and characterize their spectra. Particularly, we find a sufficient condition in terms of distances and intensities for the self-adjoint extension $H_{\alpha,X}^{(3)}$ to have $m'$ negative eigenvalues, i.e., $\kappa_-(H_{\alpha,X}^{(3)})=m'\le m$. We also give an explicit description of self-adjoint nonnegative extensions.


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