The inverse Sturm-Liouville problem with mixed boundary conditions

Details The inverse Sturm-Liouville problem with mixed boundary conditions The inverse Sturm-Liouville problem with mixed boundary conditions

2006-07-31

arxiv.org/abs/math/0607811v1

Mathematics

Spectral Theory

Scientific paper

Consider the operator $H\p=-\p''+q\p=\l\p$, $\p(0)=0$, $\p'(1)+b\p(1)=0$ acting in $L^2(0,1)$, where $q\in L^2(0,1)$ is a real potential. Let $\l_n(q,b)$, $n\ge 0$, be the eigenvalues of $H$ and $\n_n(q,b)$ be the so-called norming constants. We give a complete characterization of all spectral data $(\{\l_n\}_0^\iy;\{\n_n\}_0^\iy)$ that correspond to $(q;b)\in L^2(0,1)\ts\R$. If $b$ is fixed, then we obtain a similar characterization and parameterize the iso-spectral manifolds.

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