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Dependence of the Weyl coefficient on singular interface conditions

Published online by Cambridge University Press:  28 May 2009

Matthias Langer
Affiliation:
Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK; Email: (ml@maths.strath.ac.uk)
Harald Woracek
Affiliation:
Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstrasse 8–10/101, 1040 Wien, Austria; Email: (harald.woracek@tuwien.ac.at)
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Abstract

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We investigate the influence of interface conditions at a singularity of an indefinite canonical system on its Weyl coefficient. An explicit formula which parametrizes all possible Weyl coefficients of indefinite canonical systems with fixed Hamiltonian function is derived. This result is illustrated with two examples: the Bessel equation, which has a singular end point, and a Sturm–Liouville equation whose potential has an inner singularity, which arises from a continuation problem for a positive definite function.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2009