Journal d'Analyse Mathématique

, Volume 120, Issue 1, pp 151–224

Sturm-Liouville operators with measure-valued coefficients


    • Faculty of MathematicsUniversity of Vienna
  • Gerald Teschl
    • Faculty of MathematicsUniversity of Vienna
    • International Erwin Schrödinger Institute for Mathematical Physics

DOI: 10.1007/s11854-013-0018-x

Cite this article as:
Eckhardt, J. & Teschl, G. JAMA (2013) 120: 151. doi:10.1007/s11854-013-0018-x


We give a comprehensive treatment of Sturm-Liouville operators whose coefficients are measures, including a full discussion of self-adjoint extensions and boundary conditions, resolvents, and Weyl-Titchmarsh-Kodaira theory. We avoid previous technical restrictions and, at the same time, extend all results to a larger class of operators. Our operators include classical Sturm-Liouville operators, Sturm-Liouville operators with (local and non-local) δ and δ′ interactions or transmission conditions as well as eigenparameter dependent boundary conditions, Krein string operators, Lax operators arising in the treatment of the Camassa-Holm equation, Jacobi operators, and Sturm-Liouville operators on time scales as special cases.

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© Hebrew University Magnes Press 2013