Geodesic
Spectral Properties of the Schr\"odinger Operator with $\delta$-Distribution
Matematičeskie zametki, Tome 100 (2016) no. 2, pp. 256-269

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For the one-dimensional Schrödinger operator with $\delta$-interactions, two-sided estimates of the distribution function of the eigenvalues and a criterion for the discreteness of the spectrum in terms of the Otelbaev function are obtained. A criterion for the resolvent of the Schrödinger operator to belong to the class $\mathfrak S_p$ is established.
Keywords: Schrödinger operator, semiboundedness below of the distribution functions of eigenvalues, discreteness of the spectrum of the Schrödinger operator, point interactions. 
@article{MZM_2016_100_2_a5,
     author = {Medet Nursultanov},
     title = {Spectral {Properties} of the {Schr\"odinger} {Operator} with $\delta${-Distribution}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {256--269},
     publisher = {mathdoc},
     volume = {100},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_2_a5/}
}
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Medet Nursultanov. Spectral Properties of the Schr\"odinger Operator with $\delta$-Distribution. Matematičeskie zametki, Tome 100 (2016) no. 2, pp. 256-269. http://geodesic.mathdoc.fr/item/MZM_2016_100_2_a5/