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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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