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Dependence of the Weyl coefficient on singular interface conditions

Langer, M. and Woracek, Harald (2009) Dependence of the Weyl coefficient on singular interface conditions. Proceedings of the Edinburgh Mathematical Society, 52 (2). pp. 445-487. ISSN 0013-0915

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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 parameterizes 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 endpoint, and a Sturm-Liouville equation whose potential has an inner singularity, which arises from a continuation problem for a positive definite function.