J-Inner matrix functions, interpolation and inverse problems for canonical systems, II: The inverse monodromy problem |
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Authors: | Damir Z Arov Harry Dym |
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Institution: | (1) Department of Mathematics, South-Ukranian Pedagogical University, 270020 Odessa, Ukraine;(2) Department of Mathematics, The Weizmann Institute of Science, 76100 Rehovot, Israel |
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Abstract: | This is the second of a planned sequence of papers on inverse problems for canonical systems of differential equations. It is devoted to the inverse monodromy problem for canonical integral and differential systems. In this part, which focuses on the case of a diagonal signature matrixJ, a parametrization is obtained of the set of all solutionsM (t) for the inverse problem for integral systems in terms of two chains of entire matrix valued inner functions. Special classes of solutions correspond to special choices of these chains. This theme will be elaborated upon further in a third part of this paper which will be published in a subsequent issue of this journal. There the emphasis will be on symmetries and growth conditions all of which serve to specify or restrict the chains alluded to above, from the outside, so to speak. |
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Keywords: | 30E05 30D99 34A55 34L40 47A56 47A57 |
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