Analyticity and uniform stability of the inverse singular Sturm--Liouville spectral problem

We prove that the potential of a Sturm--Liouville operator depends analytically and Lipschitz continuously on the spectral data (two spectra or one spectrum and the corresponding norming constants). We treat the class of operators with real-valued distributional potentials in the Sobolev class W^{s-1}_2(0,1), s\in[0,1].Comment: 25 page

Eigenvalue asymptotics for Sturm--Liouville operators with singular potentials

We derive eigenvalue asymptotics for Sturm--Liouville operators with singular complex-valued potentials from the space W^{\al-1}_{2}(0,1), \al\in[0,1], and Dirichlet or Neumann--Dirichlet boundary conditions. We also give application of the obtained results to the inverse spectral problem of recovering the potential from these two spectra.Comment: Final version as appeared in JF

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