Stability of the inverse transmission eigenvalue problem for the Schrödinger operator with a radial potential

Abstract

In the work, we consider the stability of the inverse transmission eigenvalue problem for the Schrödinger operator with a radial potential q∈W21[0,1]. Under the assumption that the mean value of the potential is zero and q(1 ) ≠ 0 , the local solvability and stability are obtained by Buterin et al. (Inverse Probl 36:105002, 2020), whereas they need the condition that the difference of two spectral sequences of two problems, in the sense of l2-norm, is small enough. In this paper, we shall extend their stability result by using a different method, without this condition. By using the theory of transformation operators and the properties of Riesz basis, we give the estimates for the difference of two potentials in the sense of the weak form and W21-norm, in terms of the difference of two corresponding spectral data. As a corollary, we obtain that if only finite spectral data are close enough, then the corresponding potentials are also close in the sense of the weak form.