 03435 Alexei Rybkin
 The analytic structure of the reflection coefficient, a sum rule, and a complete description of the Weyl mfunction of halfline Schr dinger operators with L₂type potentials
(42K, AMSTEX )
Sep 21, 03

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Abstract. We prove that the reflection coefficient of onedimensional Schr dinger operators with potentials supported on a halfline 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 mfunction of Dirichlet halfline Schr dinger operators with potentials q subject to:
∫∫e^{xy}q(x)q(y)dxdy<∞.
Among others, we also refine the 3/2LiebThirring inequality.
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