J. Differential Equations 257, 415-449 (2014) [DOI: 10.1016/j.jde.2014.04.005]

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

Jonathan Eckhardt, Aleksey Kostenko, Mark Malamud, and Gerald Teschl

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.

MSC2010: Primary 34L40, 81Q10; Secondary 34L05, 34L20
Keywords: Schrödinger operator, delta-prime-interaction, spectral properties

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