A special case of de Branges' theorem on the inverse monodromy problem |
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Authors: | Peter Yuditskii |
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Institution: | (1) Mathematical Division, Institute for Low Temperature Physics, Lenin's pr. 47, 310164 Kharkov, Ukraine;(2) Present address: Department of Mathematics, Michigan State University, 48824 East Lansing, MI, U.S.A. |
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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.This work was supported by the Austrian Founds zur Förderung der wissenschaftlichen Forschung, project-number P12985-TEC |
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Keywords: | 46E22 30F35 47E05 34L05 34A55 |
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