Sturm-Liouville operators with measure-valued coefficients

Abstract

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.

58 pages

References in corpus (6)

• Weyl-Titchmarsh Theory for Schroedinger Operators with Strongly Singular Potentials
• Uniqueness for Inverse Sturm-Liouville Problems with a Finite Number of Transmission Conditions
• On the substitution rule for Lebesgue-Stieltjes integrals
• Resolvent convergence of Sturm-Liouville operators with singular potentials
• Sturm-Liouville operators on time scales
• On the connection between the Hilger and Radon--Nikodym derivatives

Cited by in corpus (15)

• Uniqueness for Inverse Sturm-Liouville Problems with a Finite Number of Transmission Conditions
• The inverse spectral problem for indefinite strings
• The inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data
• Spectral asymptotics for canonical systems
• One-dimensional Schroedinger operators with delta-prime-interactions on Cantor-type sets
• Spectral Theory for Systems of Ordinary Differential Equations with Distributional Coefficients
• On the absolutely continuous spectrum of generalized indefinite strings
• A Lagrangian view on complete integrability of the two-component Camassa-Holm system
• On the spectral theory for first-order systems without the unique continuation property
• On Fourier expansions for systems of ordinary differential equations with distributional coefficients
• Green's functions for first-order systems of ordinary differential equations without the unique continuation property
• Asymptotics of the Weyl Function for Schrödinger Operators with Measure-Valued Potentials
• Trace formulas and inverse spectral theory for generalized indefinite strings
• Generalized indefinite strings with purely discrete spectrum
• On eigenvalue bounds for a general class of Sturm-Liouville operators