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Self-adjoint boundary conditions for singular Sturm-Liouville problems and the computation of m-functions for Bessel, Legendre, and Laguerre operators

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No logo availableBanff International Research Station (BIRS) for Mathematical Innovation and Discovery
 Gesztesy, Fritz

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Self-adjoint boundary conditions for singular Sturm-Liouville problems and the computation of m-functions for Bessel, Legendre, and Laguerre operators
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We extend the classical boundary values for (general, three-coefficient) regular Sturm-Liouville operators on compact intervals to the singular case as long as the associated minimal operator is bounded from below, utilizing principal and nonprincipal solutions of the underlying differential equation. We derive the singular Weyl-Titchmarsh-Kodaira m-function and illustrate the theory with the examples of the Bessel, Legendre, and Laguerre (resp., Kummer) operators.