By Damir Z. Arov,Harry Dym

This principally self-contained remedy surveys, unites and extends a few twenty years of study on direct and inverse difficulties for canonical platforms of crucial and differential equations and comparable platforms. 5 easy inverse difficulties are studied during which the most a part of the given info is both a monodromy matrix; an enter scattering matrix; an enter impedance matrix; a matrix valued spectral functionality; or an asymptotic scattering matrix. The corresponding direct difficulties also are taken care of. The booklet contains introductions to the speculation of matrix valued complete capabilities, reproducing kernel Hilbert areas of vector valued complete features (with distinct cognizance to 2 vital areas brought through L. de Branges), the speculation of J-inner matrix valued capabilities and their program to bitangential interpolation and extension difficulties, that are used independently for classes and seminars in research or for self-study. a few examples are provided to demonstrate the theory.

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