Stability Criteria for the Weyl m-Function |
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Authors: | Amrein W O Pearson D B |
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Institution: | (1) Department of Theoretical Physics, University of Geneva, CH-1211 Geneva 4, Switzerland;(2) Department of Mathematics, University of Hull, Cottingham Road, Hull, U.K |
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Abstract: | This paper presents a new approach to spectral theory for theSchrödinger Operator on the half-line. Solutions of nonlinearRiccati-type equations related to the Schrödinger equation at realspectral parameter are characterised by means of their clusteringproperties as is varied. A family of solutions exhibiting aso-called -clustering property is shown to imply precise estimatesfor the complex boundary value of the Weyl m-function and thespectral measure, and leads to an analysis of the absolutely continuouscomponent of the spectral measure in terms of stability criteria for thecorresponding Riccati equations. |
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Keywords: | m-function Schrö dinger operator spectrum |
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