J-inner matrix functions, interpolation and inverse problems for canonical systems, III: More on the inverse monodromy problem
Copyright policy )J-inner matrix functions, interpolation and inverse problems for canonical systems, III: More on the inverse monodromy problem
The paper is a continuation of the study by \textit{D. Z. Arov} and \textit{H. Dym} [Integral Equations Oper. theory 29, No. 4, 373-454 (1997; Zbl 0902.30026)] (Part I), Part II ibid. 36, No. 1, 11-70 (2000; Zbl 0951.30029)]. The part I, Foundations, established a parametrization of the set of all solutions to the inverse monodromy for canonical integral systems in terms of two continuous chains of matrix valued inner functions in a special case. In this Part III the inverse of the monodromy problem for canonical systems of integral and differential equations was studied. The solutions of this inverse problem for homogeneous or unicellular classes, the maximal chain-type case, the one-side case, the symplectic case, and the real case were discussed. The inverse monodromy problem for symplectic, real, and real symplectic monodromy matrices was analysed.
Inverse problems involving ordinary differential equations, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), Moment problems and interpolation problems in the complex plane, Linear operator methods in interpolation, moment and extension problems, Entire and meromorphic functions of one complex variable, and related topics, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
Inverse problems involving ordinary differential equations, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), Moment problems and interpolation problems in the complex plane, Linear operator methods in interpolation, moment and extension problems, Entire and meromorphic functions of one complex variable, and related topics, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
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