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One-dimensional Schrödinger operators with -interactions on Cantor-type sets

Eckhardt, Jonathan, Kostenko, Aleksey, Malamud, Mark and Teschl, Gerald 2014. One-dimensional Schrödinger operators with -interactions on Cantor-type sets. Journal of Differential Equations 257 (2) , pp. 415-449. 10.1016/j.jde.2014.04.005

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We introduce a novel approach for defining a δ′-interaction on a subset of the real line of Lebesgue measure zero which is based on Sturm–Liouville differential expression with measure coefficients. This enables us to establish basic spectral properties (e.g., self-adjointness, lower semiboundedness and spectral asymptotics) of Hamiltonians with δ′-interactions concentrated on sets of complicated structures.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Publisher: Elsevier
ISSN: 0022-0396
Last Modified: 25 Feb 2019 11:23

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