Inverse eigenvalue problem via finite-difference three-diagonal Schrödinger operator

نویسندگان

  • Vladimir M. Chabanov
  • Boris N. Zakhariev
چکیده

In present article the self-contained derivation of eigenvalue inverse problem results is given by using a discrete approximation with three-diagonal SturmLiouville operator on a finite interval. It is demonstrated that inverse problem procedure is nothing else than well known Gram-Schmidt orthonormalization in Euclidean space for special vectors numbered by space coordinate index. All the results of usual inverse problem with continuous coordinate are reobtained by employing a limiting procedure, including reproducing an equivalent equation in partial derivatives for the solutions of the inverse problem equations – the Goursat problem which guarantees the solvability of the inverse problem equations. MSC-class: 65F18

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تاریخ انتشار 2003