Regular singular Sturm-Liouville operators and their zeta-determinants

Abstract

We consider Sturm-Liouville operators on the line segment [0, 1] with general regular singular potentials and separated boundary conditions. We establish existence and a formula for the associated zeta-determinant in terms of the Wronski- determinant of a fundamental system of solutions adapted to the boundary conditions. This generalizes the earlier work of the first author, treating general regular singular potentials but only the Dirichlet boundary conditions at the singular end, and the recent results by Kirsten-Loya-Park for general separated boundary conditions but only special regular singular potentials.

38 pages, 2 figures; Completely revised according to the referees comprehensive suggestions; v3: minor corrections, accepted for publication in Journal of Functional Analysis

References in corpus (10)

• Weyl-Titchmarsh Theory for Schroedinger Operators with Strongly Singular Potentials
• Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators
• On the Determinant of One-Dimensional Elliptic Boundary Value Problems
• Unusual poles of the $\zeta$-functions for some regular singular differential operators
• The very unusual properties of the resolvent, heat kernel, and zeta function for the operator $-d^2/d{r}^2-1/(4r^2)$
• Functional Determinants for Regular-Singular Laplace-type Operators
• Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone
• The analytic torsion of a cone over a sphere
• The Intersection R-Torsion for Finite Cone
• The Metric Anomaly of Analytic Torsion at the Boundary of an Even Dimensional Cone

Cited by in corpus (10)

• On the Singular Weyl-Titchmarsh Function of Perturbed Spherical Schroedinger Operators
• Symmetrized Perturbation Determinants and Applications to Boundary Data Maps and Krein-Type Resolvent Formulas
• Spectral Asymptotics for Perturbed Spherical Schrödinger Operators and Applications to Quantum Scattering
• Spectral Functions for Regular Sturm-Liouville Problems
• Zeta-determinants of Sturm-Liouville operators with quadratic potentials at infinity
• The exotic heat-trace asymptotics of a regular-singular operator revisited
• A New Example of the Effects of a Singular Background on the Zeta Function
• Singular Schroedinger operators as self-adjoint extensions of n-entire operators
• Heat-trace asymptotics for edge Laplacians with algebraic boundary conditions
• A class of $n$-entire Schrödinger operators