Journal d'Analyse Mathématique

, Volume 120, Issue 1, pp 151–224 | Cite as

Sturm-Liouville operators with measure-valued coefficients

Article

Abstract

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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Copyright information

© Hebrew University Magnes Press 2013

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaWienAustria
  2. 2.International Erwin Schrödinger Institute for Mathematical PhysicsWienAustria

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