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Inverse spectral results in Sobolev spaces for the AKNS operator with partial informations on the potentials

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  • We consider the AKNS (Ablowitz-Kaup-Newell-Segur) operator on the unit interval with potentials belonging to Sobolev spaces in the framework of inverse spectral theory. Precise sets of eigenvalues are given in order that they, together with the knowledge of the potentials on the side $(a,1)$ and partial informations on the potential on $(a-\varepsilon,a)$ for some arbitrary small $\varepsilon>0$, determine the potentials entirely on $(0,1)$. Naturally, the smaller is $a$ and the more partial informations are known, the less is the number of the needed eigenvalues.
    Mathematics Subject Classification: Primary: 34A55; Secondary: 34L40, 47E05.

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