A generalized spectral theory for continuous metrics on compact Riemann surfaces

Abstract

We extend the spectral theory of generalized Laplacians to continuous metrics on compact Riemann surfaces. We define a holomorphic analytic torsion for any continuous metric. As an application of this theory, we partly recover some results of the theory of Bessel functions, for instance, Lommel's theorem on the reality of the zeros of Bessel functions of order exceeding −1.