Reconstruction of Potential Function for Diffusion Operator

Abstract

Inverse spectral problem for diffusion operator consists in reconstruction of this operator by its spectrums and norming constants. In this paper, we are concerned with inverse problem for diffusion operator using a new kind of spectral data that is known as nodal points. We give a reconstruction of q as a limit of a sequence of functions whose nth term is dependent only eigenvalue and its associated nodal data. The technique we use to obtain the results is an adaptation of the method discussed in the reference Chen et al. (Proc. Ann. Math. Ser. 2002; 130:2319–2324).