Spectrally determined singularities in a potential with an inverse square initial term

We study the inverse spectral problem for Bessel type operators with potential (v(x)): (H_\kappa=-\partial_x^2+\frac{k}{x^2}+v(x)). The is assumed smooth in ((0,R)) and an asymptotic expansion powers logarithms as (x\rightarrow 0^+, v(x)=O(x^\alpha), \alpha >-2). Specifically we show that coefficients of are spectrally determined. This achieved by computing trace resolvent this operator which determined elaborating relation potential, through singular asymptotics lemma.