### Abstract

Language | English |
---|---|

Pages | 445-487 |

Number of pages | 43 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 52 |

Issue number | 2 |

DOIs | |

Publication status | Published - 28 May 2009 |

### Fingerprint

### Keywords

- indefinite canonical system
- Weyl coefficient
- singular potential

### Cite this

*Proceedings of the Edinburgh Mathematical Society*,

*52*(2), 445-487. https://doi.org/10.1017/S0013091507000806

}

*Proceedings of the Edinburgh Mathematical Society*, vol. 52, no. 2, pp. 445-487. https://doi.org/10.1017/S0013091507000806

**Dependence of the Weyl coefficient on singular interface conditions.** / Langer, M.; Woracek, Harald.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Dependence of the Weyl coefficient on singular interface conditions

AU - Langer, M.

AU - Woracek, Harald

PY - 2009/5/28

Y1 - 2009/5/28

N2 - 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.

AB - 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.

KW - indefinite canonical system

KW - Weyl coefficient

KW - singular potential

U2 - 10.1017/S0013091507000806

DO - 10.1017/S0013091507000806

M3 - Article

VL - 52

SP - 445

EP - 487

JO - Proceedings of the Edinburgh Mathematical Society

T2 - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 2

ER -