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. First of all, this enables us to explain some unusual properties of Hamiltonians with \delta'-interactions (for example, approximation by Hamiltonians with smooth potentials). Furthermore, we establish basic spectral properties (e.g., self-adjointness, lower semiboundedness and spectral asymptotics) of Hamiltonians with \delta'-interactions concentrated on sets of complicated structures.
The talk is based on joint work with J. Eckhardt, M. Malamud and G. Teschl.