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Dependence of the Weyl coefficient on singular interface conditions

Part of: Boundary value problems Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  28 May 2009

Matthias Langer  and
Harald Woracek
Matthias Langer
Affiliation:
Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK; Email: ([email protected])
Harald Woracek
Affiliation:
Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstrasse 8–10/101, 1040 Wien, Austria; Email: ([email protected])
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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.

Keywords

indefinite canonical systemWeyl coefficientsingular potential

MSC classification

Secondary: 34B20: Weyl theory and its generalizations 34B30: Special equations (Mathieu, Hill, Bessel, etc.) 46C20: Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 2 , June 2009 , pp. 445 - 487
Copyright
Copyright © Edinburgh Mathematical Society 2009