Article
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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