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

Abstract

We introduce a novel approach for defining a ${\delta }^{\prime }$-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 ${\delta }^{\prime }$-interactions concentrated on sets of complicated structures.

30 pages

References in corpus (2)

• Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials
• Schrödinger operators with delta and delta'-potentials supported on hypersurfaces

Cited by in corpus (4)

• On the absolutely continuous spectrum of generalized indefinite strings
• On absence of bound states for weakly attractive ${\delta }^{\prime }$-interactions supported on non-closed curves in ${\mathbb{R}}^2$
• Generalized indefinite strings with purely discrete spectrum
• On the absolutely continuous spectrum of generalized indefinite strings II