В работе доказана единственность восстановления оператора Штурма-Лиувилля c разрывными коэффициентами по спектральным данным и дан алгоритм построения потенциала. Ключевые слова: обратная задача, оператор Штурма-Лиувилля, собственные значения.

The paper proves the existence of the transformation operator for summable functions and finds the analogy of the formula for the potential with the transformation operator in the given case.

This paper investigates the inverse scattering problem for a discrete Dirac system on the entire line with coefficients that stabilize to zero in one direction. We develop an algorithm for solving the inverse problem of reconstruction of coefficients. We derive a necessary and a sufficient condition on the scattering data so that the inverse problem is uniquely solvable.

In this study, we consider the domains of the minimal and maximal operators generated of singular differential-expression-type Sturm-Liouville and obtain all self-adjoint extensions of the operator in terms of boundary conditions.