The analytic structure of the reflection coefficient, a sum rule and a complete description of the Weyl m-function of half-line Schrodinger operators with L2-type potentials

We prove that the reflection coefficient of one-dimensional Schrodinger operators with potentials supported on a half-line can he represented in the upper half-plane as the quotient of a contractive analytic function and a properly regularized Blaschke product. We apply this fact to obtain a new trace formula and trace inequality for the reflection coefficient that yields a description of the Weyl m-function of Dirichlet half-fine Schrodinger operators with slowly decaying potentials q subject to integral(e-x vertical bar x-y vertical bar)(R2)q(x)q(y) dx dy < infinity. Among others, we also refine the 3/2-Lieb-Thirring inequality.