J. d'Analyse Math. 120, 151-224 (2013) [DOI: 10.1007/s11854-013-0018-x]

Sturm-Liouville operators with measure-valued coefficients

Jonathan Eckhardt and Gerald Teschl

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.

MSC2000: Primary 34B20, 34L05; Secondary 34B24, 47A10
Keywords: Sturm-Liouville operators, measure coefficients, spectral theory, strongly singular potentials

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