STABILITY OF THE PROBLEM OF RECOVERING THE STURM-LIOUVILLE OPERATOR FROM THE SPECTRAL FUNCTION

Abstract

We consider a differential operator generated by a Sturm-Liouville operation on the linear manifold of finite twice-differentiable functions satisfying the boundary condition . Let be the spectral function of this operator. From , as is well known, we can recover the operator , i.e. the number and the function . Let be the set of operators for which We now investigate how much information about the operator can be obtained if its spectral function is known only for values of on a finite interval.In the present article we obtain estimates for the difference in the potentials , in the boundary parameters and in the solutions of the corresponding differential equations under the condition that the spectral functions of the two operators in coincide on a finite interval.Bibliography of 7 entries.