The reconstruction of Sturm-Liouville operators

@article{Rundell1992TheRO,
  title={The reconstruction of Sturm-Liouville operators},
  author={W. Rundell and P. Sacks},
  journal={Inverse Problems},
  year={1992},
  volume={8},
  pages={457-482}
}
  • W. Rundell, P. Sacks
  • Published 1992
  • Mathematics
  • Inverse Problems
  • The authors give a constructive algorithm for the inverse Sturm-Liouville operator in non-potential form. They emphasize the unknown impedance case, i.e. the recovery of the coefficient a(x) in (a(x)u'(x))'+ lambda a(x)u(x)=0 from spectral data. It is shown that many of the formulations of this problem are equivalent to solving an overdetermined boundary value problem for a certain hyperbolic operator. An iterative procedure for solving this latter problem is developed and numerical examples… CONTINUE READING
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