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- Title
1-D Schrödinger Operators with Local Interactions on a Discrete Set with Unbounded Potential.
- Authors
Ananieva, Aleksandra
- Abstract
We study spectral properties of the one-dimensional Schrödinger operators $$ {\mathrm{H}}_{\mathrm{X},\alpha, \mathrm{q}}:=-\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}+\mathrm{q}(x)+{\varSigma_x}_{{}_n}\in X{\alpha}_n\delta \left(x-{x}_n\right) $$ with local interactions, d = 0, and an unbounded potential q being a piecewise constant function, by using the technique of boundary triplets and the corresponding Weyl functions. Under various sufficient conditions for the self-adjointness and discreteness of Jacobi matrices, we obtain the condition of self-adjointness and discreteness for the operator H .
- Subjects
SCHRODINGER operator; DISCRETE geometry; CONSTANTS of integration; WEYL space; JACOBI integral; SELFADJOINT operators
- Publication
Journal of Mathematical Sciences, 2017, Vol 220, Issue 5, p554
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-016-3200-8