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

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