One-dimensional Schroedinger operators with delta-prime-interactions on Cantor-type sets

Jonathan Eckhardt; Aleksey Kostenko; Mark Malamud; Gerald Teschl

doi:10.1016/j.jde.2014.04.005

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arXiv · 1401.7581

One-dimensional Schroedinger operators with delta-prime-interactions on Cantor-type sets

Jonathan Eckhardt·Aleksey Kostenko·Mark Malamud·Gerald Teschl

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Abstract

We introduce a novel approach for defining a $\delta'$-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 $\delta'$-interactions concentrated on sets of complicated structures.

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Jonathan Eckhardt, Aleksey Kostenko, Mark Malamud, Gerald Teschl. 2014-01-29. One-dimensional Schroedinger operators with delta-prime-interactions on Cantor-type sets. https://doi.org/10.1016/j.jde.2014.04.005

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