AMOUR, Laurent; FAUPIN, Jérémy; RAOUX, Thierry

doi:10.1063/1.3087426

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AMOUR, Laurent
Laboratoire de Mathématiques de Reims [LMR]

FAUPIN, Jérémy
Institut de Mathématiques de Bordeaux [IMB]

RAOUX, Thierry
Laboratoire de Mathématiques de Reims [LMR]

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Journal of Mathematical Physics. 2009-03-09, vol. 50, p. 033505

American Institute of Physics (AIP)

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We pursue the analysis of the Schrödinger operator on the unit interval in inverse spectral theory initiated in the work of Amour and Raoux ["Inverse spectral results for Schrödinger operators on the unit interval with potentials in $L^p$ spaces", Inverse Probl. 23, 2367 (2007)]. While the potentials in the work of Amour and Raoux belong to $L^1$ with their difference in $L^p$, $1 \le p < +\infty$, we consider here potentials in $W^{k,1}$ spaces having their difference in $W^{k, p}$, where $1 \le p \le + \infty$, $k \in \{0 , 1 , 2\}$. It is proved that two potentials in $W^{k,1}([0,1])$ being equal on $[a,1]$ are also equal on $[0,1]$ if their difference belongs to $W^{k, p}([0,a])$ and if the number of their common eigenvalues is sufﬁciently high. Naturally, this number decreases as the parameter $a$ decreases and as the parameters $k$ and $p$ increase.< Réduire

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Inverse spectral results for Schrödinger operators on the unit interval with partial information given on the potentials

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