Geodesic
One-dimensional Schr\"odinger operator with $\delta$-interactions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 2, pp. 87-91

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The one-dimensional Schrödinger operator $\mathrm{H}_{X,\alpha}$ with $\delta$-interactions on a discrete set is studied in the framework of the extension theory. Applying the technique of boundary triplets and the corresponding Weyl functions, we establish a connection of these operators with a certain class of Jacobi matrices. The discovered connection enables us to obtain conditions for the self-adjointness, lower semiboundedness, discreteness of the spectrum, and discreteness of the negative part of the spectrum of the operator $\mathrm{H}_{X,\alpha}$.
Keywords: Schrödinger operator, point interactions, self-adjointness, lower semiboundedness, discreteness. 
@article{FAA_2010_44_2_a8,
     author = {A. S. Kostenko and M. M. Malamud},
     title = {One-dimensional {Schr\"odinger} operator with $\delta$-interactions},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {87--91},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2010_44_2_a8/}
}
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A. S. Kostenko; M. M. Malamud. One-dimensional Schr\"odinger operator with $\delta$-interactions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 2, pp. 87-91. http://geodesic.mathdoc.fr/item/FAA_2010_44_2_a8/