## Abstract

We give a new proof of a special case of de Branges' theorem on the inverse monodromy problem: when an associated Riemann surface is of Widom type with Direct Cauchy Theorem. The proof is based on our previous result (with M.Sodin) on infinite dimensional Jacobi inversion and on Levin's uniqueness theorem for conformal maps onto comb-like domains. Although in this way we can not prove de Branges' Theorem in full generality, our proof is rather constructive and may lead to a multi-dimensional generalization. It could also shed light on the structure of invariant subspaces of Hardy spaces on Riemann surfaces of infinite genus.

Original language | English |
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Pages (from-to) | 229-252 |

Number of pages | 24 |

Journal | Integral Equations and Operator Theory |

Volume | 39 |

Issue number | 2 |

DOIs | |

State | Published - 2001 |

Externally published | Yes |

### Bibliographical note

Funding Information:This work was supported by the Austrian Founds zur FSrderung der wissenschaftlichen Forschung, project-number P12985-TEC

### Funding

This work was supported by the Austrian Founds zur FSrderung der wissenschaftlichen Forschung, project-number P12985-TEC

Funders | Funder number |
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Kommission zur Förderung der wissenschaftlichen Forschung |