Stability of the Reconstruction Discontinuous Sturm-Liouville Problem

Abstract

In this work, we study stability of the inverse spectral problem for the Sturm-Liouville operator -D²+q with discontinuity boundary conditions inside a finite closed interval. We use the method which is given by Ryabushko for regular Sturm-Liouville operator in <cite>ryb</cite> to obtain stability results. These results give a bound for the difference between the spectral functions of associated problems. In addition, we give asymptotic representation of the eigenvalues and a formula for the representation of the norming constants by two spectra.

Keywords

• Discontinuity,stability,spectral function,Sturm-Liouville

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