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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 $$q$$.
##### MSC:
 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)
##### Keywords:
Sturm-Liouville operators; inverse spectral problem
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##### References:
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