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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

Alexei Rybkin
Affiliation:
Department of Mathematical Sciences, University of Alaska Fairbanks, PO Box 756660, Fairbanks, AK 99775, USA (ffavr@uaf.edu)

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
Copyright
Copyright © Royal Society of Edinburgh 2006

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