Spectral problem for diffusion operator

Abstract

In this paper, we study the inverse problem with two given spectra for diffusion operator on a finite interval. Making use of the Levitan's method, we show that the kernels (A)over-tilde(x,t) - A(x,t) and (B)over-tilde(x,t) = B(x,t) and are generalized degeneracy in the extended sense.