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Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations by Harry Dym, Damir Z. Arov

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8Inverse monodromy problems

This chapter is devoted to the inverse monodromy problem for canonical integral and differential systems. The given data for this problem is a mvf

image

and the objective is either to find a regular canonical integral system with monodromy matrix U or a regular canonical differential system with monodromy matrix U.

A fundamental theorem of V.P. Potapov (Theorem 2.11) guarantees that both of these problems have at least one solution. In particular, Potapov’s theorem guarantees that there exists a continuous nondecreasing m × m mvf M(t) on an interval [0, d] with M(0) = 0 such that U(λ) is equal to the monodromy matrix

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