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Recovery of the Schrödinger operator on the half-line from a particular set of eigenvalues. (English) Zbl 1391.34040
Let \(\lambda_j(q,h_n),\; n\geq 1,\) be an eigenvalue of the Sturm-Liouville operator \[ -y''(x)+q(x)y(x)=\lambda y(x),\; x>0, \] \[ (1+x)q(x)\in L(0,\infty),\quad y'(0)-h_ny(0)=0, \] with fixed \(j\). It is proved that if the sequence \(\{h_n\}\) has a limit point, then the specification of \(\lambda_j(q,h_n)\), \(n\geq 1\), uniquely determines \(q\).
34A55 Inverse problems involving ordinary differential equations
34B24 Sturm-Liouville theory
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
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