Schr\"odinger Operators with $\delta$-interactions in a Space of Vector-Valued Functions

Abstract

We study spectral properties of Schr\"odinger operators with $\delta$-interactions on a semi-axis by using the theory of boundary triplets and the corresponding Weyl functions. We establish a connection between spectral properties (deficiency indices, self-adjointness, semiboundedness, discreteness of spectra, resolvent comparability etc.) of Schr\"odinger operators with point interactions and a special class of block Jacobi matrices.