06-18 Fr d ric Serier (LMJL)

Inverse spectral problem for singular AKNS operator on [0,1]. (403K, Latex) Jan 23, 06

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Abstract. We consider an inverse spectral problem for a class of singular AKNS operators $H_a, a\in\N$ with an explicit singularity. We construct for each $a\in\N$, a standard map $\lambda^a\times\kappa^a$ with spectral data $\lambda^a$ and some norming constant $\kappa^a$. For $a=0$, $\lambda^a\times\kappa^a$ was known to be a local coordinate system on $\lr\times\lr$. Using adapted transformation operators, we extend this result to any non-negative integer $a$, give a description of isospectral sets and we obtain a Borg-Levinson type theorem.

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