Direct and inverse spectral theory of singular left-definite Sturm-Liouville operators

Details Direct and inverse spectral theory of singular left-definite Sturm-Liouville operators Direct and inverse spectral theory of singular left-definite Sturm-Liouville operators

2011-10-24

arxiv.org/abs/1110.5195v1

Mathematics

Spectral Theory

42 pages

Scientific paper

We give a comprehensive treatment of strongly singular Sturm-Liouville operators in the left-definite setting. In particular, we describe all self-adjoint realizations in a modified Sobolev space and develop Weyl-Titchmarsh theory for these operators (with separate boundary conditions). Finally, we apply generalizations of de Branges' subspace ordering theorem to obtain inverse uniqueness results for the associated spectral measure. The results can be applied to solve the inverse spectral problem associated with the Camassa-Holm equation.

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