Spectral Functions for Regular Sturm-Liouville Problems

Abstract

In this paper we provide a detailed analysis of the analytic continuation of the spectral zeta function associated with one-dimensional regular Sturm-Liouville problems endowed with self-adjoint separated and coupled boundary conditions. The spectral zeta function is represented in terms of a complex integral and the analytic continuation in the entire complex plane is achieved by using the Liouville-Green (or WKB) asymptotic expansion of the eigenfunctions associated with the problem. The analytically continued expression of the spectral zeta function is then used to compute the functional determinant of the Sturm-Liouville operator and the coefficients of the asymptotic expansion of the associated heat kernel.

LaTex, 27 pages

References in corpus (3)

• Casimir Effect in the Presence of External Fields
• The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the type $I{\times }_{f}N$
• The Casimir Effect for Generalized Piston Geometries

Cited by in corpus (5)

• Ground state modulations in the $\mathbb{C}{P}^{N-1}$ model
• The spectral $\zeta$-function for quasi-regular Sturm--Liouville operators
• The Casimir Effect for Thick Pistons
• Virial coefficients expressed by heat kernel coefficients
• The exotic structure of the spectral $\zeta$-function for the Schrödinger operator with Pöschl--Teller potential