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Unique determination of a system by a part of the monodromy matrix

Abstract

First-order ODE systems on a finite interval with nonsingular diagonal matrix B multiplying the derivative and integrable off-diagonal potential matrix Q are considered. It is proved that the matrix Q is uniquely determined by the monodromy matrix W(λ). In the case B = B*, the minimum number of matrix entries of W(λ) sufficient to uniquely determine Q is found.

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Correspondence to M. M. Malamud.

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Translated from Funktsional′nyi Analiz i Ego Prilozheniya, Vol. 49, No. 4, pp. 33–49, 2015 Original Russian Text Copyright © by M. M. Malamud

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Malamud, M.M. Unique determination of a system by a part of the monodromy matrix. Funct Anal Its Appl 49, 264–278 (2015). https://doi.org/10.1007/s10688-015-0115-y

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  • DOI: https://doi.org/10.1007/s10688-015-0115-y

Keywords

  • ODE systems
  • canonical systems
  • monodromy matrix
  • inverse problems for ODE systems