On inverse problem for singular Sturm-Liouville operator from two spectra - Panakhov, E. S.; Yilmazer, R. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
In the paper, an inverse problem with two given spectra for second order differential operator with singularity of type 2r + l(l+1)r^2 (here, l is a positive integer or zero) at zero point is studied. It is well known that two spectra {λ_n} and {μ_n} uniquely determine the potential function q(r) in a singular Sturm-Liouville equation defined on interval (0, π]. One of the aims of the paper is to prove the generalized degeneracy of the kernel K(r, s). In particular, we obtain a new proof of Hochstadt’s theorem concerning the structure of the difference q(r) - q(r).