M. Langer and H. Woracek,
Dependence of the Weyl coefficient on singular interface conditions,
Proc. Edinburgh Math. Soc. (2) 52 (2009), 445–487
Abstract:
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.