Inverse problems for matrix Sturm-Liouville operators

Abstract

Inverse spectral problems for nonselfadjoint matrix Sturm-Liouville differential operators on a finite interval and on the half-line are studied. As a main spectral characteristic, we introduce the so-called Weyl matrix and prove that the specification of the Weyl matrix uniquely determines the matrix potential and the coefficients of the boundary conditions. Moreover, for a finite interval, we also study the inverse problems of recovering matrix Sturm-Liouville operators from discrete spectral data (eigenvalues and “weight” numbers) and from a system of spectra. The results thus obtained are natural generalizations of the classical results in inverse problem theory for scalar Sturm-Liouville operators.

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Dedicated to the memory of B. M. Levitan

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Yurko, V. Inverse problems for matrix Sturm-Liouville operators. Russ. J. Math. Phys. 13, 111–118 (2006). https://doi.org/10.1134/S1061920806010110

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Keywords

  • Boundary Condition
  • Inverse Problem
  • Spectral Data
  • Spectral Characteristic
  • Differential Operator