Regular singular Sturm-Liouville operators and their zeta-determinants

Details Regular singular Sturm-Liouville operators and their zeta-determinants Regular singular Sturm-Liouville operators and their zeta-determinants

2010-05-03

arxiv.org/abs/1005.0368v3

J. Funct. Anal. 261 (2011), 408--450

Mathematics

Spectral Theory

38 pages, 2 figures; Completely revised according to the referees comprehensive suggestions; v3: minor corrections, accepted f

Scientific paper

10.1016/j.jfa.2011.03.011

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.

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