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This article is cited in 32 scientific papers (total in 32 papers)
Brief communications
One-dimensional Schrödinger operator with $\delta$-interactions
A. S. Kostenkoa, M. M. Malamudb a School of Mathematical Sciences, Dublin Institute of Technology
b Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences, Donetsk
Abstract:
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.
Received: 08.07.2009
Citation:
A. S. Kostenko, M. M. Malamud, “One-dimensional Schrödinger operator with $\delta$-interactions”, Funktsional. Anal. i Prilozhen., 44:2 (2010), 87–91
Linking options:
https://www.mathnet.ru/eng/faa2982https://doi.org/10.4213/faa2982 https://www.mathnet.ru/eng/faa/v44/i2/p87
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Abstract page: | 882 | Full-text PDF : | 346 | References: | 101 | First page: | 60 |
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