Electronic Resource
Springer
Mathematical physics, analysis and geometry
1 (1998), S. 193-221
ISSN:
1572-9656
Keywords:
m-function
;
Schrödinger operator
;
spectrum
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
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 λ are characterised by means of their clusteringproperties as λ is varied. A family of solutions exhibiting aso-called δ-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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009759202730
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