Inverse spectral problems for Bessel operators

We study the inverse spectral problem for a class of Bessel operators given in L2(0,1)L2(0,1) by the differential expression−(ddx−κx−v)(ddx+κx+v) with κ∈Nκ∈N and a real-valued function v∈Lp(0,1)v∈Lp(0,1), p∈[1,∞)p∈[1,∞), subject to various boundary conditions. We describe completely the spectral data of these operators, i.e., the spectra and corresponding norming constants, and give the algorithm of reconstruction of v from the spectral data.