# inverse spectral problem, how to recover the function $q(x)$

given the problem of a second order sturm liouville operator

$$- \frac{d^{2}}{dx^{2}}y(x)+q(x)y(x)=zy(x)$$

with the boundary conditions $y(0)=0=y(\infty)$

if i know the spectral meassure function $\sigma (x) =\sum_{\lambda_{n} \le x}1$

i can reconstruct the inverse of the potential $q^{-1}(x)$

however my questio is how i use the Gelfand Levitan marchenko theory to reconstruct the potential $q(x)$ thanks.

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