Inverse spectral problems for Sturm–Liouville operators with partial information

[[abstract]]In this paper, we study the inverse spectral problems for Sturm–Liouville operators with Robin boundary conditions and show that if the potential q on the interval [0,α] for some α∈[0,1) is given a priori, then the potential q on the whole interval [0,1] can be uniquely determined by a subset of pairs of eigenvalues and the weight numbers of the corresponding eigenvalues or by parts of two spectra.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]GB

Inverse spectral problems for Sturm-Liouville operators with singular potentials

The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants. The reconstruction algorithm is presented and its stability proved. Also, the set of all possible spectral data is explicitly described and the isospectral sets are characterized.Comment: Submitted to Inverse Problem

Analyticity and uniform stability in the inverse spectral problem for Dirac operators

We prove that the inverse spectral mapping reconstructing the square integrable potentials on [0,1] of Dirac operators in the AKNS form from their spectral data (two spectra or one spectrum and the corresponding norming constants) is analytic and uniformly stable in a certain sense.Comment: 19 page