arXiv subjects

Frédéric Serier

Publications and source records attributed to Frédéric Serier.

2 recordsLinked to original sources

arXiv2006

Inverse spectral problem for singular AKNS operator on [0,1]

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 $λ^a\timesκ^a$ with spectral data $λ^a$ and some norming constant $κ^a$. For $a=0$, $λ^a\timesκ^a$ 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.

math.SP↗

arXiv2005

Inverse spectral problem for radial Schrödinger operator on [0, 1]

For a class of singular Sturm-Liouville equations on the unit interval with explicit singularity $a(a + 1)/x^2, a \in \mathbb{N}$, we consider an inverse spectral problem. Our goal is the global parametrization of potentials by spectral data noted by $λ^a$, and some norming constants noted by $κ^a$. For $a = 0$ and $a=1$, $λ^a\times κ^a$ was already known to be a global coordinate system on $\lr$. With the help of transformation operators, we extend this result to any non-negative integer $a$ and give a description of isospectral sets.

math.SP↗