Abstract
The method (Martynyuk and Pivovarchik, Inverse Probl. 26(3):035011, 2010) of recovering the potential of the Sturm–Liouville equation on a half of the interval by the spectrum of a boundary value problem and by the restriction of the potential onto the other half of the interval is used for treating the missing eigenvalue problem (Trans. Am. Math. Soc. 352:2765–3789, 2000, J. R. Astr. Soc. 62:41–48, 1980, J. Math. Pures Appl. 91:468–475, 2009, J. Math. Soc. Japan 38:39–65, 1986). The latter arises in the case of the half-inverse (Hochstadt–Lieberman) problem with Robin boundary conditions and lies in the fact that in many cases all the eigenvalues but one are needed to recover the potential and the Robin condition at one of the ends.
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Pivovarchik, V. On the Hald–Gesztesy–Simon Theorem. Integr. Equ. Oper. Theory 73, 383–393 (2012). https://doi.org/10.1007/s00020-012-1966-8
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DOI: https://doi.org/10.1007/s00020-012-1966-8