Sturm-Liouville operators with measure-valued coefficients

Details Sturm-Liouville operators with measure-valued coefficients Sturm-Liouville operators with measure-valued coefficients

2011-05-18

arxiv.org/abs/1105.3755v1

Mathematics

Spectral Theory

58 pages

Scientific paper

We give a comprehensive treatment of Sturm-Liouville operators with measure-valued coefficients including, a full discussion of self-adjoint extensions and boundary conditions, resolvents, and Weyl-Titchmarsh 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, 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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