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.

Introduction A bit of physical motivation Preliminaries on ODEs The 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 endpoint The 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 solutions Renormalized oscillation theory Perturbative oscillation criteria and perturbative Hardy-type inequalities Boundary data maps Spectral zeta functions and computing traces and determinants for Sturm-Liouville operators The singular problem on $(a,b)\subseteq\mathbb{R}$ revisited Four-coefficient Sturm-Liouville operators and distributional potential coefficients Epilogue: Applications to some partial differnetial equations of mathematical physics Basic facts on linear operators Basics of spectral theory Classes of bounded linear operators Extensions of symmetric operators Elements of sesquilinear forms Basics of Nevanlinna-Herglotz functions Bessel functions in a nutshell Bibliography Author index List of symbols Subject index