One-dimensional Schroedinger operators with delta-prime-interactions on   Cantor-type sets
  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. 
Jonathan Eckhardt, Aleksey Kostenko, Mark Malamud, and Gerald Teschl
math.SP math-ph math.MP