Sturm-Liouville Operators, Their Spectral Theory, and Some Applications

Fritz Gesztesy, Baylor University, Waco, TX, Roger Nichols, The University of Tennessee at Chattanooga, TN, and Maxim Zinchenko, University of New Mexico, Albuquerque, NM.

• IntroductionA bit of physical motivationPreliminaries on ODEsThe regular problem on a compact interval $[a,b]\subset\mathbb{R}$The singular problem on $(a,b)\subseteq \mathbb{R}$The spectral function for a problem with a regular endpointThe 2 x 2 spectral matrix function in the presence of two singular interval endpoints for the problem on $(a,b)\subseteq\mathbb{R}$Classical oscillation theory, principal solutions, and nonprinicpal solutionsRenormalized oscillation theoryPerturbative oscillation criteria and perturbative Hardy-type inequalitiesBoundary data mapsSpectral zeta functions and computing traces and determinants for Sturm-Liouville operatorsThe singular problem on $(a,b)\subseteq\mathbb{R}$ revisitedFour-coefficient Sturm-Liouville operators and distributional potential coefficientsEpilogue: Applications to some partial differnetial equations of mathematical physicsBasic facts on linear operatorsBasics of spectral theoryClasses of bounded linear operatorsExtensions of symmetric operatorsElements of sesquilinear formsBasics of Nevanlinna-Herglotz functionsBessel functions in a nutshellBibliographyAuthor indexList of symbolsSubject index