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Inverse Scattering of Canonical Systems and Their Evolution

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Abstract

In this work we present an analogue of the inverse scattering for canonical systems using theory of vessels and associated to them completely integrable systems. Analytic coefficients fits into this setting, significantly expanding the class of functions for which the inverse scattering exists. We also derive an evolutionary equation, arising from canonical systems, which describes an evolution of the logarithmic derivative of the tau function, associated to these systems.

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Notes

  1. At the paper [11] a similar result is proved for functions symmetric with respect to the unit circle, but it can be translated using Calley transform into \(S^*(-\bar{\lambda }) \sigma _1 S(\lambda ) = \sigma _1\) and was done in [4, 22].

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  1. Drexel University, Phialdelphia, PA, USA

    Andrey Melnikov

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  1. Andrey Melnikov
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Correspondence to Andrey Melnikov.

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Communicated by Irene Sabadini.

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Melnikov, A. Inverse Scattering of Canonical Systems and Their Evolution. Complex Anal. Oper. Theory 9, 793–819 (2015). https://doi.org/10.1007/s11785-014-0391-1

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