could someone give me some info about inverse spectral proble ??(adsbygoogle = window.adsbygoogle || []).push({});

my doubt is the following, let us suppose we know the spectrum or more precisely the value of the function/distribution

[tex] Z(u)= \sum _{n} Cos( u \lambda _n) [/tex] is known for u >0 , so i can calculate Z(u) exactly for every positive u

my next assumption is that this set of eigenvalues (lambda) belongs to the self-adjoint operator

[tex] -D^2y(x) + W(x)y(x) [/tex]

my problem is that i do not know what W(x) is , is ther using the inverse spectral theory a method to obtain a differential , integral or other kind of equation for W(x) ??

another possible question , let us suppose that [tex] -D^2y(x) + W(x)y(x) [/tex] is a 1-D Scrodinger equation associated to a scattering problem, then how could i recover W(x) ??? , if possible give me analytic (approximate) solutions please, thank you very much.

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# Inverse spectral problem

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