A Schrödinger operator with a δ′‐interaction on a Cantor set and Krein–Feller operators

DOI10.1002/mana.200310371zbMath1105.47039OpenAlexW1972239331MaRDI QIDQ5467033

Sergio A. Albeverio, Leonid P. Nizhnik

Publication date: 23 May 2006

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200310371

zbMATH Keywords

Schrödinger operatorsCantor setpoint interactionnegative eigenvaluessingular interactionKrein-Feller operatorboundary value data

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Sturm-Liouville theory (34B24) Spectrum, resolvent (47A10) Perturbation theory of linear operators (47A55) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of ordinary differential operators (47E05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items

\(\delta^{\prime}\)-interaction as a limit of a thin Neumann waveguide with transversal window ⋮ Distribution theory for Schrödinger’s integral equation ⋮ Two-parametric ${\delta'}$ -interactions: approximation by Schrödinger operators with localized rank-two perturbations ⋮ Schrödinger operators with \(\delta^{\prime}\)-interactions and the Kreĭn-Stieltjes string ⋮ Schrödinger operators with nonlocal point interactions ⋮ Sturm-Liouville operators with measure-valued coefficients ⋮ Inverse uniqueness results for Schrödinger operators using de Branges theory ⋮ Construction of self‐adjoint differential operators with prescribed spectral properties ⋮ Finitely additive functions in measure theory and applications ⋮ Stochastics and dynamics of fractals ⋮ Spectral theory of semibounded Schrödinger operators with \(\delta'\)-interactions ⋮ One-dimensional Schrödinger operators with \(\delta'\)-interactions on Cantor-type sets ⋮ Resolvents of self-adjoint extensions with mixed boundary conditions ⋮ 1-D Schrödinger operators with local point interactions on a discrete set

Cites Work

• Unnamed Item
• Unnamed Item
• Generalized Second-Order Differential Operators, Corresponding Gap Diffusions and Superharmonic Transformations
• On the spectral functions of the string