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<p>This is an essay about my joint work with Harry Dym over more than 30 years. The results of our joint work were presented in a number of our papers and in three monographs, published in the years 2008, 2012 and 2018. They are devoted to the development of the theory of <i>J</i>-contractive (mainly <i>J</i>-inner) matrix-valued functions and related topics: (1) generalized (bitangential) Schur and Carathéodory interpolation problems, as well as generalized Krein extension problems for positive and helical matrix valued functions and accelerants; (2) direct and inverse scattering, impedance, asymptotic scattering and spectral problems for differential and integral systems of equations; (3) de Branges reproducing kernel Hilbert spaces corresponding to <i>J</i>-inner matrix functions and the so-called de Branges matrices; (4) generalized Krein prediction problems for continuous time stochastic <i>p</i>-dimensional weak stationary processes and for processes with weak stationary increments.</p>

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On My Joint Work with Harry Dym

  • 期刊论文

  • 发表日期：

    2025年6月22日

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  • Damir Z. Arov

摘要

This is an essay about my joint work with Harry Dym over more than 30 years. The results of our joint work were presented in a number of our papers and in three monographs, published in the years 2008, 2012 and 2018. They are devoted to the development of the theory of J-contractive (mainly J-inner) matrix-valued functions and related topics: (1) generalized (bitangential) Schur and Carathéodory interpolation problems, as well as generalized Krein extension problems for positive and helical matrix valued functions and accelerants; (2) direct and inverse scattering, impedance, asymptotic scattering and spectral problems for differential and integral systems of equations; (3) de Branges reproducing kernel Hilbert spaces corresponding to J-inner matrix functions and the so-called de Branges matrices; (4) generalized Krein prediction problems for continuous time stochastic p-dimensional weak stationary processes and for processes with weak stationary increments.