J. d'Analyse Math. 120, 151-224 (2013) [DOI: 10.1007/s11854-013-0018-x]
Sturm-Liouville operators with measure-valued coefficients
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.