Inverse spectral results for Schrödinger operators on the unit interval with potentials in L^P spaces

Details Inverse spectral results for Schrödinger operators on the unit interval with potentials in L^P spaces Inverse spectral results for Schrödinger operators on the unit interval with potentials in L^P spaces

2007-10-21

arxiv.org/abs/0710.3915v1

Inverse Problems 23 (2007) 2367-2373

Mathematics

Spectral Theory

Scientific paper

10.1088/0266-5611/23/6/006

We consider the Schr\"odinger operator on $[0,1]$ with potential in $L^1$. We
prove that two potentials already known on $[a,1]$ ($a\in(0,{1/2}]$) and having
their difference in $L^p$ are equal if the number of their common eigenvalues
is sufficiently large. The result here is to write down explicitly this number
in terms of $p$ (and $a$) showing the role of $p$.

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