Alexei Rybkin
The analytic structure of the reflection coefficient, a sum rule, and a complete description of the Weyl m-function of half-line Schr dinger operators with L₂-type potentials
(42K, AMS-TEX )

ABSTRACT.  We prove that the reflection coefficient of one-dimensional Schr dinger operators with potentials supported on a half-line can be 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 sum rule and sum inequality for the reflection coefficient that yields an exhaustive description of the Weyl m-function of Dirichlet half-line Schr dinger operators with potentials q subject to: 
 &#8747;&#8747;e^{-|x-y|}q(x)q(y)dxdy<&#8734;. 
Among others, we also refine the 3/2-Lieb-Thirring inequality.