The analytic structure of the reflection coefficient, a sum rule and a complete description of the Weyl m-function of half-line Schrödinger operators with L2-type potentials
Published online by Cambridge University Press: 30 July 2007
Abstract
We prove that the reflection coefficient of one-dimensional Schrödinger 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 trace formula and trace inequality for the reflection coefficient that yields a description of the Weyl m-function of Dirichlet half-line Schrödinger operators with slowly decaying potentials q subject to Among others, we also refine the 3/2-Lieb-Thirring inequality.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 3 , June 2006 , pp. 615 - 632
- Copyright
- Copyright © Royal Society of Edinburgh 2006
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