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 X,α,q.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 13, No. 1, pp. 28–67, January–March, 2016.
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Ananieva, A.Y. 1-D Schrödinger Operators with Local Interactions on a Discrete Set with Unbounded Potential. J Math Sci 220, 554–583 (2017). https://doi.org/10.1007/s10958-016-3200-8
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DOI: https://doi.org/10.1007/s10958-016-3200-8